what is diagrammatic representation of data

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Diagrammatic Presentation of Data

The diagrammatic presentation of data gives an immediate understanding of the real situation to be defined by the data in comparison to the tabular presentation of data or textual representations. It translates the highly complex ideas included in numbers into a more concrete and quickly understandable form pretty effectively. Diagrams may be less certain but are much more efficient than tables in displaying the data. There are many kinds of diagrams in general use. Amongst them the significant ones are the following:

(i) Geometric diagram

(ii) Frequency diagram

(iii) Arithmetic line graph

Also check: Meaning and Objective of Tabulation

Basics of Diagrammatic Presentation

Concept of Diagrammatic Presentation

• It is a technique of presenting numeric data through pictograms, cartograms, bar diagrams, and pie diagrams. It is the most attractive and appealing way to represent statistical data. Diagrams help in visual comparison and they have a bird’s eye view.
• Under pictograms, we use pictures to present data. For example, if we have to show the production of cars, we can draw cars. Suppose the production of cars is 40,000, we can show it by a picture having four cars, where 1 car represents 10,000 units.
• Under cartograms, we make use of maps to show the geographical allocation of certain things.
• Bar diagrams are rectangular and placed on the same base. Their heights represent the magnitude/value of the variable. The width of all the bars and the gaps between the two bars are kept the same.
• Pie diagram is a circle that is subdivided or partitioned to show the proportion of various components of the data.
• Out of the given diagrams, only one-dimensional bar diagrams and pie diagrams are there in our scope.

General Guidelines

Title: Every diagram must be given a suitable title which should be small and self-explanatory.

Size: The size of the diagram should be appropriate, i.e., neither too small nor too big.

Paper used: Diagrams are generally prepared on blank paper.

Scale: Under one-dimensional diagrams, especially bar diagrams, the y-axis is more important from the point of view of the decision of scale because we represent magnitude along this axis.

Index: When two or more variables are presented and different types of line/shading patterns are used to distinguish, an index must be given to show their details.

Selection of proper type of diagram: It is very important to select the correct type of diagram to represent data effectively.

Advantages of Diagrammatic Presentation

(1) Diagrams are attractive and impressive:   The data presented in the form of diagrams can attract the attention of even a common man.

(2) Easy to remember:    (a)  Diagrams have a great memorising effect. (b)  The picture created in mind by the diagrams last much longer than those created by figures presented through the tabular forms.

(3) Diagrams save time : (a)  They present complex mass data in a simplified manner. (b)  The data presented in the form of diagrams can be understood by the user very quickly.

(4) Diagrams simplify data:   Diagrams are used to represent a huge mass of complex data in a simplified and intelligible form which is easy to understand.

(5) Diagrams are useful in making comparison:   It becomes easier to compare two sets of data visually by presenting them through diagrams.

(6) More informative :   Diagrams not only depict the characteristics of data but also bring out other hidden facts and relations which are not possible from the classified and tabulated data.

Types of One-Dimensional Diagram

One-dimensional diagram is a diagram in which only the length of the diagram is considered. It can be drawn in the form of a line or various types of bars.

The following are the types of one-dimensional diagram.

(1) Simple bar diagram

Simple bar diagram consists of a group of rectangular bars of equal width for each class or category of data.

(2) Multiple bar diagram

This diagram is used when we have to make a comparison between two or more variables like income and expenditure, import and export for different years, marks obtained in different subjects in different classes, etc.

(3) Subdivided bar diagram

This diagram is constructed by subdividing the bars in the ratio of various components.

(4) Percentage bar diagram

The subdivided bar diagram presented on a percentage basis is known as the percentage bar diagram.

(5) Broken-scale bar diagram

This diagram is used when the value of one observation is very high as compared to the other.

To gain space for the smaller bars of the series, the larger bars may be broken.

The value of each bar is written at the top of the bar.

(6) Deviation bar diagram

Deviation bars are used to represent net changes in the data like net profit, net loss, net exports, net imports, etc.

Meaning of Pie Diagram

A pie diagram is a circle that is divided into sections. The size of each section indicates the magnitude of each component as a part of the whole.

Steps involved in constructing pie diagram

• Convert the given values into percentage form and multiply it with 3.6’ to get the amount of angle for each item.
• Draw a circle and start the diagram at the 12 O‘clock position.
• Take the highest angle first with the protector (D) and mark the lower angles successively.
• Shade different angles differently to show distinction in each item.

Solved Questions

Q.1. Why is a diagrammatic presentation better than tabulation of data?

It makes the data more attractive as compared to tabulation and helps in visual comparison.

Q.2. Why do media persons prefer diagrammatic presentation of data?

Because it has an eye-catching effect and a long-lasting impact upon its readers/viewers.

Q.3. What will be the degree of an angle in the pie diagram if a family spends 50% of its income in food?

(50 ÷ 100) X 360 (Or) 50 x 3.6 = 180’

Q.4. Which bar diagram is used to show two or more characteristics of the data?

Multiple bar diagram

Q.5. Mention the sum of all the angles formed at the centre of a circle.

Q.6. Name a bar diagram where the height of all the bars is the same.

Percentage bar diagram

Q.7. Which diagram can be used to depict various components of a variable?

Subdivided bar diagram

Q.8. What is a multiple bar diagram?

A multiple bar diagram is one that shows more than one characteristic of data.

Q.9. Which bar diagram is used to represent the net changes in data?

Deviation bar diagram

Q.10. What is the other name of the subdivided bar Diagram?

Component bar diagram

The above-mentioned concept is for CBSE Class 11 Statistics for Economics – Diagrammatic Presentation of Data. For solutions and study materials, visit our website or download the app for more information and the best learning experience.

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Diagrammatic Presentation Of Data

Introduction.

The diagrammatic representation also helps in having a bird’s eye view or overall view of the differentiation of data. It is a norm to present statistical data in the form of diagrams so that it becomes easier to comprehend and understand them. Therefore, diagrammatic representation is an important tool in statistics.

What is a Diagrammatic Presentation of Data?

Diagrammatic representation refers to a representation of statistical data in the form of diagrams. The diagrams used in representing statistical data are geometrical figures, such as lines, bars, and circles. The intention of using geometrical figures in statistical presentation is to make the study more interesting and easy to understand. Diagrammatic representations are widely used in statistics, economics, and many other fields of study.

Types of Diagrammatic Presentations of Data

Various types of diagrammatic representations of data depend on the dataset and the particular statistical elements in them. Data presentation can be made in different types and forms.

These can be broadly classified into the following one-dimensional types −

Line Diagram

In a line diagram, straight lines are used to indicate various parameters. Here, a line represents the sequence of data associated with the changing of a particular variable.

Properties of Line Diagram −

The Lines are either in vertical or horizontal directions.

There may be uniform scaling but this is not mandatory.

The lines that connect the data points offer the statistical representation of data.

The following is an example of a line diagram that shows profits in Rs crore from 2002 till 2008. Profit in 2002 was Rs 5 Crore while in 2008 it was Rs 24 Crore.

Bar Diagram

Bar diagrams have rectangular shapes of equal width that represent statistical data in a straightforward manner. Bar diagrams are one of the most widely used diagrammatic representations.

Properties of Bar Diagram −

The Bars can be vertical or horizontal in directions.

All bars in a diagram have a uniform width.

All the Bars have a common and same base.

The height or width of the Bar shows the required value.

The following is an example of a Bar Chart that has time on the X axis and profits on the Y axis.

Also known as a "circle chart" , the pie chart divides the circular statistical graphic into sectors or sections to illustrate the numerical data. Each sector in the circle denotes a proportionate part of the whole. Pie-chart works the best at the time when we want to denote the composition of something. In most cases, the pie chart replaces other diagrammatic representations, such as the bar graph, line plots, histograms, etc.

In practice, the various sections in a pie chart are derived according to their ratio to the total area of the circle. Then according to their individual contributions, sections are divided into parts derived from 360 degrees of the circle.

Advantages of Diagrammatic Presentation of Data

Easier to understand.

Pictorial representations are usually easier to understand than statistical text or representation in tabular form. One can easily understand which portion or part has more contribution toward the overall dataset. This helps in understanding the data better.

The creators of diagrams usually keep the simplicity of presentation in mind to offer more information to readers. That is why diagrams are easier to comprehend than texts and tables.

More attractive

Pictorial or diagrammatic representations of datasets are more attractive than normal representations. As colors and various other tools can be incorporated into diagrams, they become more attractive and comprehensible for the readers.

Moreover, as diagrams can be made more interactive with the help of computer graphics, they have become more acceptable and attractive currently.

Simpler presentations

Data can be presented more simply in diagrammatic form. Both extensive unstable data and smaller complex data can be represented by diagrammatic representations more easily. This helps statisticians offer more value to their findings.

Comparison is easier

When two or more data are compared, it is easier to do so in pictorial form. As diagrams clearly show the portion of data consumed, it can be easily understood from the diagrams which part of the data is consuming more area in the diagrams. This can help one to understand the real differences through pictorial comparison.

Universal acceptance

Diagrammatic representation of data is used in many fields of study, such as statistics, science, commerce, economics, etc. So, the diagrams are accepted universally and hence are used everywhere.

Moreover, since there are the same procedures for forming diagrams, the representations mean the same thing to everyone. So, there is nothing to alter when we obtain the diagrams to check the real values. It helps analysts solve problems universally.

Improvement in presentation

Diagrammatic representations improve the overall representation of data to a large extent. As the data is classified into several groups and presented in a systematic manner in diagrams, the whole presentation of data gets improved during the diagrammatic representation.

Moreover, as diagrams can be made more interactive than texts or tables, diagrammatic presentations are one step ahead in presenting the data in a simpler yet recognizable manner.

More organized and classified data

To represent data in diagrams, they must be organized and classified into comprehensive categories. This helps the data to be organized in a given fashion which makes them orderly and creates a sequence. This in turn helps realize diagrammatic data better than text forms.

Relevance Diagrammatic Presentation of Data

Diagrams are a great way of representing data because they are visually attractive and they can make large, complex datasets look simpler. The otherwise heavy data can be simply and easily represented by line and bar diagrams, and pie charts. This makes data organization simpler and neater.

Moreover, as data must be classified before representation, one must organize them according to the norms required. So, diagrammatic representations save lots of time and resources.

Diagrams also have universal acceptance and so can be used to express data in different forms. This provides the analysts and researchers flexibility to present data in any required form.

Diagrams also remove confusion and offer a simpler tactic to present data. As no special skill has to be learned to represent data in diagrams, they can be used by most to show statistical data and results of various types of research and experiments.

Therefore, diagrammatic representation has great relevance that can be used for the benefit of economists, statisticians, marketing analysts, and a lot of other professionals.

The diagrams are a central part of statistics and their importance can be known from the fact that almost all statistical researchers use them in one way or the other. The diagrammatical representations make inferring statistical data much simpler and easier. It is a much easier way to visualize and understand data in simpler forms too.

To represent data in diagrammatic form, only a simple understanding of Mathematics is required. So, no special skills are needed to use diagrams and this makes them very popular tools for the representation of data sets. Learning how to present data in diagrams, therefore, should be a priority for everyone.

Q1. Which is the simplest diagrammatic presentation of data?

Ans. The simplest diagrammatic presentation of data is a line diagram that shows data in terms of straight lines.

Q2. What are the two characteristics of bar diagrams?

Ans. Bar diagrams have uniform width and their base remains the same.

Q3. How are the sections in a pie chart formed?

Ans. In practice, the various sections in a pie chart are derived according to their ratio to the total area of the circle. Then according to their individual contributions, sections are divided into parts derived from 360 degrees of the circle.

For example, if a section requires 25% of the presentation, it will consume  degrees on the chart.

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• CBSE Class 11 Statistics for Economics Notes

Chapter 1: Concept of Economics and Significance of Statistics in Economics

• Statistics for Economics | Functions, Importance, and Limitations

Chapter 2: Collection of Data

• Methods of Data Collection
• Sources of Data Collection | Primary and Secondary Sources
• Direct Personal Investigation: Meaning, Suitability, Merits, Demerits and Precautions
• Indirect Oral Investigation : Suitability, Merits, Demerits and Precautions
• Difference between Direct Personal Investigation and Indirect Oral Investigation
• Information from Local Source or Correspondents: Meaning, Suitability, Merits, and Demerits
• Questionnaires and Schedules Method of Data Collection
• Difference between Questionnaire and Schedule
• Qualities of a Good Questionnaire and Types of Questionnaires
• What are the Published Sources of Collecting Secondary Data?
• What Precautions should be taken before using Secondary Data?
• Two Important Sources of Secondary Data: Census of India and Reports & Publications of NSSO
• What is National Sample Survey Organisation (NSSO)?
• What is Census Method of Collecting Data?
• Sample Method of Collection of Data
• Methods of Sampling
• Father of Indian Census
• What makes a Sampling Data Reliable?
• Difference between Census Method and Sampling Method of Collecting Data
• What are Statistical Errors?

Chapter 3: Organisation of Data

• Organization of Data
• Objectives and Characteristics of Classification of Data
• Classification of Data in Statistics | Meaning and Basis of Classification of Data
• Concept of Variable and Raw Data
• Types of Statistical Series
• Difference between Frequency Array and Frequency Distribution
• Types of Frequency Distribution

Chapter 4: Presentation of Data: Textual and Tabular

• Textual Presentation of Data: Meaning, Suitability, and Drawbacks
• Tabular Presentation of Data: Meaning, Objectives, Features and Merits
• Different Types of Tables
• Classification and Tabulation of Data

Chapter 5: Diagrammatic Presentation of Data

• Diagrammatic Presentation of Data: Meaning , Features, Guidelines, Advantages and Disadvantages
• Types of Diagrams
• Bar Graph | Meaning, Types, and Examples
• Pie Diagrams | Meaning, Example and Steps to Construct
• Histogram | Meaning, Example, Types and Steps to Draw
• Frequency Polygon | Meaning, Steps to Draw and Examples
• Ogive (Cumulative Frequency Curve) and its Types
• What is Arithmetic Line-Graph or Time-Series Graph?

Diagrammatic and Graphic Presentation of Data

Chapter 6: measures of central tendency: arithmetic mean.

• Measures of Central Tendency in Statistics
• Arithmetic Mean: Meaning, Example, Types, Merits, and Demerits
• What is Simple Arithmetic Mean?
• Calculation of Mean in Individual Series | Formula of Mean
• Calculation of Mean in Discrete Series | Formula of Mean
• Calculation of Mean in Continuous Series | Formula of Mean
• Calculation of Arithmetic Mean in Special Cases
• Weighted Arithmetic Mean

Chapter 7: Measures of Central Tendency: Median and Mode

• Median(Measures of Central Tendency): Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Median for Different Types of Statistical Series
• Calculation of Median in Individual Series | Formula of Median
• Calculation of Median in Discrete Series | Formula of Median
• Calculation of Median in Continuous Series | Formula of Median
• Graphical determination of Median
• Mode: Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Mode in Individual Series | Formula of Mode
• Calculation of Mode in Discrete Series | Formula of Mode
• Grouping Method of Calculating Mode in Discrete Series | Formula of Mode
• Calculation of Mode in Continuous Series | Formula of Mode
• Calculation of Mode in Special Cases
• Calculation of Mode by Graphical Method
• Mean, Median and Mode| Comparison, Relationship and Calculation

Chapter 8: Measures of Dispersion

• Measures of Dispersion | Meaning, Absolute and Relative Measures of Dispersion
• Range | Meaning, Coefficient of Range, Merits and Demerits, Calculation of Range
• Calculation of Range and Coefficient of Range
• Interquartile Range and Quartile Deviation
• Partition Value | Quartiles, Deciles and Percentiles
• Quartile Deviation and Coefficient of Quartile Deviation: Meaning, Formula, Calculation, and Examples
• Quartile Deviation in Discrete Series | Formula, Calculation and Examples
• Quartile Deviation in Continuous Series | Formula, Calculation and Examples
• Mean Deviation: Coefficient of Mean Deviation, Merits, and Demerits
• Calculation of Mean Deviation for different types of Statistical Series
• Mean Deviation from Mean | Individual, Discrete, and Continuous Series
• Mean Deviation from Median | Individual, Discrete, and Continuous Series
• Standard Deviation: Meaning, Coefficient of Standard Deviation, Merits, and Demerits
• Standard Deviation in Individual Series
• Standard Deviation in Discrete Series
• Standard Deviation in Frequency Distribution Series
• Combined Standard Deviation: Meaning, Formula, and Example
• How to calculate Variance?
• Coefficient of Variation: Meaning, Formula and Examples
• Lorenz Curveb : Meaning, Construction, and Application

Chapter 9: Correlation

• Correlation: Meaning, Significance, Types and Degree of Correlation
• Methods of Measurements of Correlation
• Scatter Diagram Correlation | Meaning, Interpretation, Example
• Spearman's Rank Correlation Coefficient in Statistics
• Karl Pearson's Coefficient of Correlation | Assumptions, Merits and Demerits
• Karl Pearson's Coefficient of Correlation | Methods and Examples

Chapter 10: Index Number

• Index Number | Meaning, Characteristics, Uses and Limitations
• Methods of Construction of Index Number
• Unweighted or Simple Index Numbers: Meaning and Methods
• Methods of calculating Weighted Index Numbers
• Fisher's Index Number as an Ideal Method
• Fisher's Method of calculating Weighted Index Number
• Paasche's Method of calculating Weighted Index Number
• Laspeyre's Method of calculating Weighted Index Number
• Laspeyre's, Paasche's, and Fisher's Methods of Calculating Index Number
• Consumer Price Index (CPI) or Cost of Living Index Number: Construction of Consumer Price Index|Difficulties and Uses of Consumer Price Index
• Methods of Constructing Consumer Price Index (CPI)
• Wholesale Price Index (WPI) | Meaning, Uses, Merits, and Demerits
• Index Number of Industrial Production : Characteristics, Construction & Example
• Inflation and Index Number

Important Formulas in Statistics for Economics

• Important Formulas in Statistics for Economics | Class 11

Diagrammatic and graphic presentation of data means visual representation of the data. It shows a comparison between two or more sets of data and helps in the presentation of highly complex data in its simplest form. Diagrams and graphs are clear and easy to read and understand. In the diagrammatic presentation of data, bar charts, rectangles, sub-divided rectangles, pie charts, or circle diagrams are used. In the graphic presentation of data, graphs like histograms, frequency polygon, frequency curves, cumulative frequency polygon, and graphs of time series are used.

General Rules for Construction of Diagrammatic and Graphic Presentations: 

1. Chronic Number: Each outline or chart should have a chronic number. It is important to recognize one from the other.

2. Title: A title should be given to each outline or chart. From the title, one can understand what the graph or diagram is. The title ought to be brief and simple. It is normally positioned at the top.

3. Legitimate size and scale: An outline or chart ought to be of ordinary size and drawn with an appropriate scale. The scale in a chart indicates the size of the unit.

4. Neatness: Outlines should be pretty much as straightforward as could be expected. Further, they should be very perfect and clean. They ought to likewise be dropped to check out.

5. File: Each outline or chart should be joined by a record. This outlines various sorts of lines, shades or tones utilized in the graph.

6. Commentary: Commentaries might be given at the lower part of an outline. It explains specific focuses in the chart.

Merits of Diagrammatic and Graphics Presentation:

The fundamental benefits or merits of a diagrammatic and graphical representation of data are as follows:

1. To simplify the data: Outlines and charts present information in a simple manner that can be perceived by anyone without any problem. Huge volume of data can be easily presented using graphs and diagrams.

2. Appealing presentation: Outlines and charts present complex information and data in an understandable and engaging manner and leave a great visual effect. In this way, the diagrammatic and graphical representation of information effectively draws the attention of users.

3. Helps with comparison of data: With the help of outlines and charts, comparison and examination data between various arrangements of information is possible.

4. Helps in forecasting: The diagrammatic and graphical representation of information has past patterns, which helps in forecasting and making various policies for the future.

5. Saves time and labour: Charts and graphs make the complex data into a simple form, which can be easily understood by anyone without having prior knowledge of the data. It gives ready to use information, and the user can use it accordingly. In this way, it saves a lot of time and labour.

6. Universally acceptable: Graphs and diagrams are used in every field and can be easily understood by anyone. Hence they are universally acceptable.

7. Helps in decision making: Diagrams and graphs give the real data about the past patterns, trends, outcomes, etc., which helps in future preparation.

Demerits of Diagrammatic and Graphics Presentation:

The demerits of diagrammatic and graphics presentation of data are as follows:

1. Handle with care: Drawing, surmising and understanding from graphs and diagrams needs proper insight and care. A person with little knowledge of statistics cannot analyze or use the data properly.

2. Specific information: Graphs and diagrams do not depict true or precise information. They are generally founded on approximations. The information provided is limited and specific.

3. Low precision: Graphs and diagrams can give misleading results, as they are mostly based on approximation of data. Personal judgement is used to study or analyze the data, which can make the information biased. Also, data can easily be manipulated.

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• Diagrammatic Presentation of Data

Nowadays a lot of emphases is laid upon exceptional presentation of data.  All of this is because, when presented diagrammatically, data is easy to interpret with just a glance. In such a case we need to learn how to represent data diagrammatically via bar diagrams, pie charts etc.

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Bar diagrams.

As the name suggests, when data is presented in form of bars or rectangles , it is termed to be a bar diagram.

Features of a Bar

• The rectangular box in a bar diagram is known as a bar. It represents the value of a variable .
• These bars can be either vertically or horizontally arranged.
• Bars are equidistant from each other.
• Each bar originates from a common baseline or a common axis.
• The width of bars remain same but the height changes, according to the value of a variable, to denote the difference between their values.
• Unless they are in a specific order, the convention is that bars can be arranged in an ascending or descending order.

Browse more Topics under Presentation Of Data

• Textual and Tabular Presentation of Data

Types of Bar Diagrams

Simple bar diagram.

These are the most basic type of bar diagrams. A simple bar diagram represents only a single set of numerical data. Generally, simple bar diagrams are used to represent time series data for a single entity.

Generally, the Y-axis contains markings which represent the range of the value of variable whereas the X-axis contains divisions for entities like years, time periods, areas etc.

Multiple Bar Diagram

Unlike single bar diagram, a multiple bar diagram can represent two or more sets of numerical data on the same bar diagram. Generally, these are constructed to facilitate comparison between two entities like average height and average weight, birth rates and death rates etc.

Separate sets of numerical data are differentiated with the help of colour variation. By the same token of simple bar diagrams, multiple bar diagrams also have divisions on Y-axis and X-axis that represent different values of the variable and entities like year, areas etc. respectively. Note that each division on X-axis has two or more bar diagrams each according to the specified number of bars.

Sub-divided or Differential Bar Diagrams

Sub-divided bar diagrams are useful when we need to represent the total values and the contribution of various sections of the total simultaneously. The different sections are shaded with different colours in the same bar.

For example, such a bar diagram can be used to represent the varying levels of employment over the years in India and each bar can be divided into two sectors, the urban and rural. Again, here the Y-axis and X-axis represent same values as in simple and multiple bar diagrams.

Percentage Bar Diagrams

This is derived further from the subdivided bar diagrams. In this, each bar has the same height that represents 100 percent of the Y-axis in totality. Further, each bar is divided into sections based on percentages calculated according to the contribution of these sections.

Percentage bar diagrams are used when the values are really high. This is because using subdivided bar diagrams in such cases would not be easy and appropriate.

Deviation Bar Diagrams

Lastly, the deviation bar diagrams are most interesting of the lot. In such a type of bar diagram, there are both negative and positive values on the y-axis. The deviation bar diagrams are used to compare the net deviation of related variables with respect to time and location.

For example, it can be used to represent a bar diagram for savings (represented by positive deviations) and deficit (represented by negative deviations) over years.

Pie or Circular Diagrams

In addition to bar diagrams, pie diagrams are also widely used to pictorially represent data. In this, a circle is divided into various segments which are decided on the basis of percentages. Which means the circle is divided into sectors depending on various percentages.

These sectors are differentiated with the help of colours. Pie diagrams have an edge over bar diagrams because they can easily provide an overview and provides a better sense of contributions of each part. The steps for construction of a pie diagram are:

The first step involves finding out respective percentages. This is done by a simple mathematical formula to find out percentages which is –

{(Parts for the respective sector)/total parts) ×100} .

For example, if in a class of 1oo students, 30 are obese, 20 are fat and 50 are slim then the percentages will be as follows:

(30/100) × 100= 30%

(20/100) × 100= 20%

(50/100) × 100= 50%

2] A circle comprises 360 degrees. The angles that each sector will span across is decided by the given formula: (Percentage value/100)×360°

3] Finally, just plot these values according to their respective angles on a circle and give appropriate markings to complete the pie chart.

A Solved Example for You

Q:   Which among the following is not a feature of a bar in the bar diagram?

• The width is same but the heights are generally different
• They are rectangular in shape
• Bars should not be equidistant
• Each bar originates from a common baseline

Ans:   Of all the above options, option C is incorrect because conventionally the bars should be equidistant.

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• Diagrammatic Presentation of Data

Introduction - Diagrammatic Presentation of Data

Diagrams are an essential operational tool for the presentation of statistical data. They are objects, mainly geometrical figures such as lines, circles, bars, etc. Statistics elaborated with the help of diagrams make it easier and simpler, thereby enhancing the representation of any type of data.

What is Diagrammatic Representation of Data?

Representation of data assisted by diagrams to increase the simplicity of the statistics surrounding the concerned data is defined as a diagrammatic representation of data. These diagrams are nothing but the use of geometrical figures to improve the overall presentation and offer visual assistance for the reader. 

What are the Types of Diagrams used in Data Presentation?

The type of diagram suitable for data presentation solely depends on the particular dataset and its statistical elements. There are multiple types of diagrams used in data presentation. They can be broadly categorized in the following types of one-dimensional diagrams –

A. Line Diagram

Line diagram is used to represent specific data across varying parameters. A line represents the sequence of data connected against a particular variable. 

Properties of Line Diagram –

The Lines can be used in vertical and horizontal directions.

They may or may not have uniform scaling 

The line connecting the data points state the statistical representation of data.

Example: Arjun, Sayak and Mainak started monitoring their time of reporting for duty for a certain week. A-Line diagram to represent their observed data on average reporting time for those days would look like –

(Image will be Uploaded Soon)

So, as per the Line Diagram, it can be easily determined that Arjun reported for work mostly at 9:30 AM while Sayak and Mainak’s most frequent times of entry at work is 10:30 AM and 10:50 AM respectively. 

B. Bar Diagram

Bar Diagram is used mostly for the comparison of statistical data. It is one of the most straightforward representations of data with the use of rectangular objects of equal width.

Properties of Bar Diagram –

The Bars can be used in vertical and horizontal directions.

These Bars all have a uniform width.

All the Bars have a common base.

The height of the Bar usually corresponds to the required value.

Example: A dataset comparing the percentile marks obtained by Shreyasi and Monika in Science subjects in the examination can be represented with the help of a Bar diagram as –

From this diagram, we can easily compare the percentile marks obtained by Shreyasi and Monika in the subjects Mathematics, Physics, Chemistry and Computer Science. 

C. Pie Chart

To know what a Pie Diagram is, it is advised to brush up on the fundamentals of the geometrical theories and formula of a Circle. For the statistical representation of data, the sectors of a circle are used as the data points of a particular dataset. A sector is the area of a circle formed by the several divisions done by the radii of the same circle.

Example: In a recent survey, a dataset was created to figure how many participants of the survey thought that Tenure or Tenor is the correct spelling in the field of Banking . A Pie Chart would present the collected data as –

With the help of this Pie Chart, it can be easily determined that the percentage of participants in the survey who chose ‘Tenor’, to be the correct spelling of the word for use in the field of banking, is 25% whereas 45% picked ‘Tenure’ as the correct answer. 20% opted for both to be correct while 10% of them were not sure with their attempt.

Advantages of Diagrammatic Presentation

There are several advantages in the presentation of data with the various types of diagrams. They are –

1. Makes it Much Easier to Understand

The presentation of data with the help of diagrams makes it easier for everybody to understand, which thereby makes it easier to grasp the statistics behind the data presented. Diagrammatic data presentation is quite common in newspapers, magazines and even in advertising campaigns so that the common mass can understand what the data is trying to reveal. 

2. Presentation is Much Simpler

With the help of diagrams, presentation of extreme values – extensive unstable data as well as small complicated data complex can be simplified exponentially. 

3. Comparison Operations are More Interactive

Datasets that require comparison of their elements use the application of diagrams for representation. Not only is the presentation attractive, but it is also ideal for showcasing a comparison in statistics.

4. Accepted Universally

Every academic and professional field, let it be Economics, Commerce, Science, Engineering, Statistics, etc. make use of diagrams across the world. Hence, this metric of data presentation is universally accepted.

5. Improves the Representation of Data as a Whole

Statistics are incomplete if diagrams are tables that are not implemented for the presentation of data. Hence, the use of diagrams helps in the overall statistical concept of data representation.

Students who are looking forward to diving deep into the theories and principles of Diagrammatic representation of data, make sure to visit the official website of Vedantu and join a live online tutoring class!

Relevance of Diagrammatic Presentation of Data

Diagrams are visually pleasing and are a great way of representing any form of data. The heavy statistics that we generate can be easily represented via diagrams such as bar charts, pie charts etc. It makes the presentation look neater and more organized. They visually aid the reader in understanding the exact situation and are also very easy to look at.  They save a lot of time and confusion and have a universal utility .  All students must learn how to represent data through diagrams so that they can present facts and figures in an organized manner.

Does Vedantu have Anything on the Diagrammatic Presentation of Data?

Vedantu has ample study material on the diagrammatic representation of data. All students can read from Diagrammatic Presentation of Data and know more. This is available completely free of cost on the platform so that the students do not hesitate before accessing them.

FAQs on Diagrammatic Presentation of Data

1. Which are the types of diagrams used in data representation?

The types of diagrams used in the representation of data are line diagrams, bar diagrams, pie charts and a few others. These are used to represent facts as they make it easier for the students to understand certain information. More about this has been explained in the Diagrammatic Presentation of Data. This page has relevant information that the students can use to understand these diagrams. After having gone through this page, they will know how to represent certain information in the form of diagrams.

2. Are there any merits of the diagrammatic representation of data?

There are a couple of merits of the diagrammatic representation of data. Some of which is that it makes it much easier to understand data, the presentation is simpler, it becomes easier to compare and correlate, and it is universally accepted. 

This page has all the details that are needed by the students to know. It is always better to present data in the form of diagrams as it makes it much more systematic. An organized manner of depicting figures makes anything simpler to understand. 

3. Is a pie chart an accurate way of representing data diagrammatically?

In a pie chart, the sectors of a circle are used as the data points of a particular dataset. It is indeed an accurate method of representing data as the correct percentage can be found out. All students can check out the Diagrammatic Presentation of Data on Vedantu. This page has all the information that’s needed by the participants. The other forms of diagrams that can be utilized for data presentations have also been talked about. This page has been created by expert Commerce teachers who know the topic inside out and can be read by all those who wish to do well in the tests.

4. Difference between the Diagrammatic and Graphical Presentation of Data.

All graphical representations of data can be a diagram, but all diagrams are not a graph. Graphs are represented on a scale, but diagrams are required to be constructed to a scale. Construction of graphs requires two more axes, but none is a necessity in case of diagrams.

5. What are the different Types of Diagrams in Statistics?

The different types of diagrams used in statistics are line diagram, bar diagram, and pie chart. Bar diagrams can further be classified into simple bar diagrams, multiple bar diagrams and component or sub-divided bar diagrams.

Advantages and Disadvantages of Diagrammatic Representation

Looking for advantages and disadvantages of Diagrammatic Representation?

We have collected some solid points that will help you understand the pros and cons of Diagrammatic Representation in detail.

But first, let’s understand the topic:

What is Diagrammatic Representation?

What are the advantages and disadvantages of diagrammatic representation.

The following are the advantages and disadvantages of Diagrammatic Representation:

Advantages of Diagrammatic Representation

Disadvantages of diagrammatic representation.

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Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

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18 Types of Diagrams You Can Use to Visualize Data (Templates Included)

Have you ever found yourself stuck while trying to explain a complex concept to someone? Or struggling to put your idea into words?

This is where diagrams come in.

While simple text is best for highlighting figures or information, diagrams are handy for conveying complex ideas and loads of information without overwhelming your audience. They can visualize almost anything, from numerical data to qualitative relationships, making them versatile tools in numerous fields.

Whether you’re in the academe or enterprise setting, this guide is for you. We’ll explore the different types of diagrams with a brief explanation for each type, the best time to use a diagram type, and how you can use them to be a better visual storyteller and communicator. You’ll also find examples and templates for each type of diagram.

Let’s get on with it.

You can also follow along by creating a free account . Select a template to get started.

What exactly is a diagram? 

A diagram is a visual snapshot of information. Think of diagrams as visual representations of data or information that communicate a concept, idea, or process in a simplified and easily understandable way. You can also use them to illustrate relationships, hierarchies, cycles, or workflows. 

Diagrams aren’t just used to show quantitative data, such as sales earnings or satisfaction ratings with a diagram. They’re equally helpful if you want to share qualitative data. For example, a diagram could be used to illustrate the life cycle of a butterfly, showcasing each transformation stage. 

Now, let’s jump into the various types of diagrams, ranging from simple flow charts to the more complex Unified Modeling Language (UML) diagrams.

18 diagram types and when to use each type 

Whether you’re doing data analysis or need a simple visual representation of data, there is a wide array of diagrams at your fingertips. If you’re having a hard time choosing the right diagram for your data visualization needs, use the list below as a quick guide. 

1. Flowchart 

A flowchart is a type of diagram that acts as a roadmap for a process or workflow. It uses shapes and arrows to guide you through each step, making complex procedures simple to understand.

Flowcharts are best for : Simplifying complex processes into understandable stages, making it easier for your readers to follow along and see the ‘big picture”. 

2. Line graph

Line graphs , sometimes called line charts, visualizes numerical data points connected by straight lines. In a line graph or line chart, data points representing different time periods are plotted and connected by a line. This helps with easy visualization of trends and patterns.

Line graphs are best for: Representing the change of one or more quantities over time, making them excellent for tracking the progression of data points.

3. Bar chart 

A bar chart , often interchangeable with bar graphs, is a type of diagram used primarily to display and compare data. For this diagram type, rectangular bars of varying lengths represent data of different categories or groups. Each bar represents a category, and the length or height of the bar corresponds to the numeric data or quantity.

Variations of bar charts include stacked bar charts, grouped bar charts, and horizontal bar charts. 

Bar charts are best for : Comparing the frequency, count, or other measures (such as average) for different categories or groups. A bar chart is particularly useful if you want to display data sets that can be grouped into categories.

4. Circle diagram or pie chart

A pie chart is a circular diagram that represents data in slices. Each slice of the pie chart represents a different category and its proportion to the whole.

Pie charts are best for: Displaying categorical data where you want to highlight each category’s percentage of the total.

5.Venn diagrams

A Venn diagram compares the differences and similarities of groups of things. As a diagram based on overlapping circles, each circle in a Venn diagram represents a different set, and their overlap represents the intersection of the data sets. 

Venn diagrams are best for : Visualizing the relationships between different groups of things. They are helpful when you want to show areas of overlap between elements. A good example is if you want to compare the features of different products or two overlapping concepts, like in the Ikigai Venn diagram template below. Easily create your Venn diagram with Piktochart’s online Venn diagram maker .

6. Tree diagrams

A tree diagram is a diagram that starts with one central idea and expands with branching lines to show multiple paths, all possible outcomes, decisions, or steps. Each ‘branch’ represents a possible outcome or decision in a tree diagram, moving from left to right. Tree diagrams are best for : Representing hierarchy like organizational roles, evolutionary relationships, or possible outcomes of events like when a company launches a product. 

7. Organizational chart 

Organizational charts are diagrams used to display the structure of an organization. In an organizational chart, each box or node represents a different role or department, and lines connecting the boxes illustrate the lines of authority, communication, and responsibility. The chart typically starts with the highest-ranking individual or body (like a CEO or Board of Directors) at the top and branches downwards to various levels of management and individual employees.

Organizational charts are best for : Showing relationships between different members and departments in a company or organization. 

8. Gantt charts 

Gantt charts are typically used in project management to represent the timeline of a project. They consist of horizontal bars, with each bar representing a task or activity.

For this type of diagram, each chart is represented by a horizontal bar spanning from its start date to its end date. The length of the bar corresponds to the duration of the task. Tasks are listed vertically, often in the order they need to be completed. In some projects, tasks are grouped under larger, overarching activities or phases.

Gantt charts are best for : Projects where you need to manage multiple tasks that occur over time, often in a specific sequence, and may depend on each other.

9. Unified Modeling Language (UML) diagram

Software engineers use Unified Modeling Language (UML) diagrams to create standardized diagrams that illustrate the building blocks of a software system.

UML diagrams, such as class diagrams, sequence diagrams, and state diagrams, provide different perspectives on complex systems. Class diagrams depict a system’s static structure, displaying classes, attributes, and relationships. Meanwhile, sequence diagrams illustrate interactions and communication between system entities, providing insight into system functionality. 

UML diagrams are best for : Visualizing a software system’s architecture in software engineering.

10. SWOT analysis diagrams 

A SWOT analysis diagram is used in business strategy for evaluating internal and external factors affecting the organization. The acronym stands for Strengths, Weaknesses, Opportunities, and Threats. Each category is represented in a quadrant chart, providing a comprehensive view of the business landscape.

SWOT diagrams are best for : Strategic planning and decision-making. They represent data that can help identify areas of competitive advantage and inform strategy development.

Piktochart offers professionally-designed templates to create diagrams , reports , presentations , brochures , and more. Sign up for a free account today to create impressive visuals within minutes.

11. Fishbone diagram 

Fishbone diagrams, sometimes called cause-and-effect diagrams,  are used to represent the causes of a problem. They consist of a central idea, with different diagrams or branches representing the factors contributing to the problem.

Fishbone diagrams are best for : Brainstorming and problem-solving sessions.

12. Funnel chart

A funnel chart is a type of diagram used to represent stages or progress. In a funnel chart, each stage is represented by a horizontal bar, and the length of the bar corresponds to the quantity or value at that stage. The chart is widest at the top, where the quantity or value is greatest, and narrows down to represent the decrease at each subsequent stage.

Funnel charts are best for: Visual representation of the sales pipeline or data visualization of how a broad market is narrowed down into potential leads and a select group of customers.

13. SIPOC diagrams

A SIPOC diagram is used in process improvement to represent the different components of a process. The acronym stands for Suppliers, Inputs, Process, Outputs, and Customers.

SIPOC diagrams are best for: Providing a high-level view of a process which helps visualize the sequence of events and their interconnections.

14. Swimlane diagrams

Swimlane diagrams are best for mapping out complex processes that involve multiple participants or groups.

Keep in mind that each lane (which can be either horizontal or vertical) in a swimlane diagram represents a different participant or group involved in the process. The steps or activities carried out by each participant are plotted within their respective lanes. This helps clarify roles and responsibilities as well as the sequence of events and points of interaction.

Swimlane diagrams are best for : Visualizing how different roles or departments interact and collaborate throughout a workflow or process.

15. Mind maps

A mind map starts with a central idea and expands outward to include supporting ideas, related subtopics, concepts, or tasks, which can be further subdivided as needed. The branches radiating out from the central idea represent hierarchical relationships and connections between the different pieces of information in a mind map.

Mind maps are best for : Brainstorming, taking notes, organizing information, and visualizing complex concepts in a digestible format.

16. Scatter Plots

Scatter plots are used to compare data and represent the relationship between two variables. In a scatter plot, each dot represents a data point with its position along the x and y axes representing the values of two variables.

Scatter plots are best for : Observing relationships and trends between the two variables. These scatter plots are useful for regression analysis, hypothesis testing, and data exploration in various fields such as statistics, economics, and natural sciences.

17. PERT chart

PERT (Project Evaluation Review Technique) charts are project management tools used to schedule tasks. Each node or arrow represents each task, while lines represent dependencies between tasks. The chart includes task duration and earliest/latest start/end times.

Construction project managers often use PERT charts to schedule tasks like design, site prep, construction, and inspection. Identifying the critical path helps focus resources on tasks that impact the project timeline.

PERT charts are best for : Visualizing the sequence of tasks, the time required for each task, and project timelines.

18. Network diagrams

A network diagram visually represents the relationships between elements in a system or project. In network diagrams, each node represents an element, such as a device in a computer network or a task in a project. The lines or arrows connecting the nodes represent the relationships or interactions between these elements.

Network diagrams are best for: Visually representing the relationships or connections between different elements in a system or a project. They are often used in telecommunications, computer networking, project management, and organization planning.

Choosing the right diagram starts with a good understanding of your audience

Understanding your audience’s needs, expectations, and context is necessary before designing diagrams. The best diagram is not the one that looks the most impressive but the one that communicates complex information most clearly and effectively to your intended audience.

Make professional diagrams for free with no design experience with Piktochart’s online diagram maker . Sign up for free .

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DIAGRAMMATIC REPRESENTATION OF DATA

An attractive representation of statistical data is provided by charts, diagrams and pictures.

Diagrammatic representation can be used for both the educated section and uneducated section of the society. Furthermore, any hidden trend present in the given data can be noticed only in this mode of representation.

However, compared to tabulation, this is less accurate.

So if there is a priority for accuracy, we have to recommend tabulation.

We are going to consider the following types of diagrams :

1. Line diagram

2. Histogram

3. Bar diagram

4. Pie chart

Line Diagram

When the time series exhibit a wide range of fluctuations, we may think of logarithmic or ratio chart where "Log y" and not "y" is plotted against "t".

We use Multiple line chart for representing two or more related time series data expressed in the same unit and multiple – axis chart in somewhat similar situations, if the variables are expressed in different units.

The profits in thousand of dollars of an industrial house for 2002, 2003, 2004, 2005, 2006, 2007 and 2008 are 5, 8, 9, 6, 12, 15 and 24 respectively. Represent these data using a suitable diagram.

We can represent the profits for 7 consecutive years by drawing either a line diagram as given below.

Let us consider years on horizontal axis and profits on vertical axis.

For the year 2002, the profit is 5 thousand dollars. It can be written as a point (2002, 5)

In the same manner, we can write the following points for the succeeding years.

(2003, 8), (2004, 9), (2005, 6), (2006, 12), (2007, 15) and (2008, 24)

Now, plotting all these point and joining them using ruler, we can get the line diagram. 

Showing line diagram for the profit of an Industrial House during 2002 to 2008.

A two dimensional graphical representation of a continuous frequency  distribution is called a histogram.

In histogram, the bars are placed continuously side by side with no gap between  adjacent bars.

That is, in histogram rectangles are erected on the class intervals of  the distribution. The areas of rectangle are proportional to the frequencies.

Draw a histogram for the following table which represent the marks obtained by 100 students in an examination :

The class intervals are all equal with length of 10 marks.

Let us denote these class intervals along the X-axis.

Denote the number of students along the Y-axis, with appropriate scale.

The histogram is given below.

Bar Diagram

There are two types of bar diagrams namely, Horizontal Bar diagram and Vertical bar  diagram.

While horizontal bar diagram is used for qualitative data or data varying over  space, the vertical bar diagram is associated with quantitative data or time series data.

Bars i.e. rectangles of equal width and usually of varying lengths are drawn either  horizontally or vertically.

We consider Multiple or Grouped Bar diagrams to compare  related series. Component or sub-divided Bar diagrams are applied for representing data  divided into a number of components. Finally, we use Divided Bar charts or Percentage

Bar diagrams for comparing different components of a variable and also the relating of  the components to the whole. For this situation, we may also use Pie chart or Pie diagram  or circle diagram.

Example : 

The total number of runs scored by a few players in one-day match is given.

Draw bar graph for the above data.

In a pie chart, the various observations or components are represented by the sectors of a circle and the whole circle represents the sum of the value of all the components .Clearly, the total angle of 360° at the center of the circle is divided according to the values of the components .

The central angle of a component is

=  [Value of the component / Total value] x 360°

Sometimes, the value of the components are expressed in percentages. In such cases,

=  [Percentage value of the component / 100] x 360°

The number of hours spent by a school student on various activities on a working day, is given below. Construct a pie chart using the angle measurement.

Draw a pie chart to represent the above information.

We may calculate the central angles for various components as follows :

From the above table, clearly, we obtain the required pie chart as shown below.

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Data Representation: Definition, Types, Examples

Data Representation: Data representation is a technique for analysing numerical data. The relationship between facts, ideas, information, and concepts is depicted in a diagram via data representation. It is a fundamental learning strategy that is simple and easy to understand. It is always determined by the data type in a specific domain. Graphical representations are available in many different shapes and sizes.

In mathematics, a graph is a chart in which statistical data is represented by curves or lines drawn across the coordinate point indicated on its surface. It aids in the investigation of a relationship between two variables by allowing one to evaluate the change in one variable’s amount in relation to another over time. It is useful for analysing series and frequency distributions in a given context. On this page, we will go through two different types of graphs that can be used to graphically display data. Continue reading to learn more.

Data Representation in Maths

Definition: After collecting the data, the investigator has to condense them in tabular form to study their salient features. Such an arrangement is known as the presentation of data.

Any information gathered may be organised in a frequency distribution table, and then shown using pictographs or bar graphs. A bar graph is a representation of numbers made up of equally wide bars whose lengths are determined by the frequency and scale you choose.

The collected raw data can be placed in any one of the given ways:

• Serial order of alphabetical order
• Ascending order
• Descending order

Data Representation Example

Example: Let the marks obtained by \(30\) students of class VIII in a class test, out of \(50\)according to their roll numbers, be:

\(39,\,25,\,5,\,33,\,19,\,21,\,12,41,\,12,\,21,\,19,\,1,\,10,\,8,\,12\)

\(17,\,19,\,17,\,17,\,41,\,40,\,12,41,\,33,\,19,\,21,\,33,\,5,\,1,\,21\)

The data in the given form is known as raw data or ungrouped data. The above-given data can be placed in the serial order as shown below:

Now, for say you want to analyse the standard of achievement of the students. If you arrange them in ascending or descending order, it will give you a better picture.

Ascending order:

\(1,\,1,\,5,\,5,\,8,\,10,\,12,12,\,12,\,12,\,17,\,17,\,17,\,19,\,19\)

\(19,\,19,\,21,\,21,\,21,\,25,\,33,33,\,33,\,39,\,40,\,41,\,41,\,41\)

Descending order:

\(41,\,41,\,41,\,40,\,39,\,33,\,33,33,\,25,\,21,\,21,\,21,\,21,\,19,\,19\)

\(19,\,19,\,17,\,17,\,17,\,12,\,12,12,\,12,\,10,\,8,\,5,\,5,1,\,1\)

When the raw data is placed in ascending or descending order of the magnitude is known as an array or arrayed data.

Graph Representation in Data Structure

A few of the graphical representation of data is given below:

• Frequency distribution table

Pictorial Representation of Data: Bar Chart

The bar graph represents the ​qualitative data visually. The information is displayed horizontally or vertically and compares items like amounts, characteristics, times, and frequency.

The bars are arranged in order of frequency, so more critical categories are emphasised. By looking at all the bars, it is easy to tell which types in a set of data dominate the others. Bar graphs can be in many ways like single, stacked, or grouped.

Graphical Representation of Data: Frequency Distribution Table

A frequency table or frequency distribution is a method to present raw data in which one can easily understand the information contained in the raw data.

The frequency distribution table is constructed by using the tally marks. Tally marks are a form of a numerical system with the vertical lines used for counting. The cross line is placed over the four lines to get a total of \(5\).

Consider a jar containing the different colours of pieces of bread as shown below:

Construct a frequency distribution table for the data mentioned above.

Graphical Representation of Data: Histogram

The histogram is another kind of graph that uses bars in its display. The histogram is used for quantitative data, and ranges of values known as classes are listed at the bottom, and the types with greater frequencies have the taller bars.

A histogram and the bar graph look very similar; however, they are different because of the data level. Bar graphs measure the frequency of the categorical data. A categorical variable has two or more categories, such as gender or hair colour.

Graphical Representation of Data: Pie Chart

The pie chart is used to represent the numerical proportions of a dataset. This graph involves dividing a circle into different sectors, where each of the sectors represents the proportion of a particular element as a whole. Thus, it is also known as a circle chart or circle graph.

Graphical Representation of Data: Line Graph

A graph that uses points and lines to represent change over time is defined as a line graph. In other words, it is the chart that shows a line joining multiple points or a line that shows the link between the points.

The diagram illustrates the quantitative data between two changing variables with the straight line or the curve that joins a series of successive data points. Linear charts compare two variables on the vertical and the horizontal axis.

General Rules for Visual Representation of Data

We have a few rules to present the information in the graphical representation effectively, and they are given below:

• Suitable Title:  Ensure that the appropriate title is given to the graph, indicating the presentation’s subject.
• Measurement Unit:  Introduce the measurement unit in the graph.
• Proper Scale:  To represent the data accurately, choose an appropriate scale.
• Index:  In the Index, the appropriate colours, shades, lines, design in the graphs are given for better understanding.
• Data Sources:  At the bottom of the graph, include the source of information wherever necessary.
• Keep it Simple:  Build the graph in a way that everyone should understand easily.
• Neat:  You have to choose the correct size, fonts, colours etc., in such a way that the graph must be a model for the presentation of the information.

Solved Examples on Data Representation

Q.1. Construct the frequency distribution table for the data on heights in \(({\rm{cm}})\) of \(20\) boys using the class intervals \(130 – 135,135 – 140\) and so on. The heights of the boys in \({\rm{cm}}\) are: 

Ans: The frequency distribution for the above data can be constructed as follows:

Q.2. Write the steps of the construction of Bar graph? Ans: To construct the bar graph, follow the given steps: 1. Take a graph paper, draw two lines perpendicular to each other, and call them horizontal and vertical. 2. You have to mark the information given in the data like days, weeks, months, years, places, etc., at uniform gaps along the horizontal axis. 3. Then you have to choose the suitable scale to decide the heights of the rectangles or the bars and then mark the sizes on the vertical axis. 4. Draw the bars or rectangles of equal width and height marked in the previous step on the horizontal axis with equal spacing. The figure so obtained will be the bar graph representing the given numerical data.

Q.3. Read the bar graph and then answer the given questions: I. Write the information provided by the given bar graph. II. What is the order of change of the number of students over several years? III. In which year is the increase of the student maximum? IV. State whether true or false. The enrolment during \(1996 – 97\) is double that of \(1995 – 96\)

Ans: I. The bar graph represents the number of students in class \({\rm{VI}}\) of a school during the academic years \(1995 – 96\,to\,1999 – 2000\). II. The number of stcccccudents is changing in increasing order as the heights of bars are growing. III. The increase in the number of students in uniform and the increase in the height of bars is uniform. Hence, in this case, the growth is not maximum in any of the years. The enrolment in the years is \(1996 – 97\, = 200\). and the enrolment in the years is \(1995 – 96\, = 150\). IV. The enrolment in \(1995 – 97\,\) is not double the enrolment in \(1995 – 96\). So the statement is false.

Q.4. Write the frequency distribution for the given information of ages of \(25\) students of class VIII in a school. \(15,\,16,\,16,\,14,\,17,\,17,\,16,\,15,\,15,\,16,\,16,\,17,\,15\) \(16,\,16,\,14,\,16,\,15,\,14,\,15,\,16,\,16,\,15,\,14,\,15\) Ans: Frequency distribution of ages of \(25\) students:

Q.5. There are \(20\) students in a classroom. The teacher asked the students to talk about their favourite subjects. The results are listed below:

By looking at the above data, which is the most liked subject? Ans: Representing the above data in the frequency distribution table by using tally marks as follows:

From the above table, we can see that the maximum number of students \((7)\) likes mathematics.

Also, Check –

• Diagrammatic Representation of Data

In the given article, we have discussed the data representation with an example. Then we have talked about graphical representation like a bar graph, frequency table, pie chart, etc. later discussed the general rules for graphic representation. Finally, you can find solved examples along with a few FAQs. These will help you gain further clarity on this topic.

FAQs on Data Representation

Q.1: How is data represented? A: The collected data can be expressed in various ways like bar graphs, pictographs, frequency tables, line graphs, pie charts and many more. It depends on the purpose of the data, and accordingly, the type of graph can be chosen.

Q.2: What are the different types of data representation? A : The few types of data representation are given below: 1. Frequency distribution table 2. Bar graph 3. Histogram 4. Line graph 5. Pie chart

Q.3: What is data representation, and why is it essential? A: After collecting the data, the investigator has to condense them in tabular form to study their salient features. Such an arrangement is known as the presentation of data. Importance: The data visualization gives us a clear understanding of what the information means by displaying it visually through maps or graphs. The data is more natural to the mind to comprehend and make it easier to rectify the trends outliners or trends within the large data sets.

Q.4: What is the difference between data and representation? A: The term data defines the collection of specific quantitative facts in their nature like the height, number of children etc., whereas the information in the form of data after being processed, arranged and then presented in the state which gives meaning to the data is data representation.

Q.5: Why do we use data representation? A: The data visualization gives us a clear understanding of what the information means by displaying it visually through maps or graphs. The data is more natural to the mind to comprehend and make it easier to rectify the trends outliners or trends within the large data sets.

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Diagrammatic Presentation of Data

• First Online: 24 August 2018

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The most important function of science of statistics is to simplify the complexity of quantitative data and to make them easily understandable. Numeric figures are usually avoided by common man, but pictures, diagrams, and graphs always attract our attention. Diagrams and graphs give a “birds’ eye view” to the entire mass of statistical data that have been collected about any hypothesis. Characteristics of diagrams and rules for drawing these have been discussed with limitations and use of these. There are a variety of diagrams like dimensional drawings, pictograms, cartograms, graphs, curves, and circles or pie diagrams, which have great utility in the presentation of data.

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Rayat, C.S. (2018). Diagrammatic Presentation of Data. In: Statistical Methods in Medical Research. Springer, Singapore. https://doi.org/10.1007/978-981-13-0827-7_4

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Schematic Diagram

AI Generator

A schematic diagram is a graphical representation of a system that uses abstract, often standardized symbols and lines to depict the components and interconnections within the system. It is commonly used in fields such as electronics, engineering, and science to simplify complex concepts and facilitate understanding, design, and troubleshooting. Unlike a pictorial diagram, which shows the physical layout of components, a schematic focuses on the function and relationship of the elements, making it an essential tool for illustrating the flow of electrical circuits , data pathways, and other intricate systems.

What Is a Schematic Diagram?

A schematic diagram is a graphical representation of an electrical or electronic circuit, showcasing the components and their interconnections using standardized symbols. These diagrams are essential tools in the fields of engineering and electronics, as they simplify the understanding, troubleshooting, and construction of complex circuits.

Schematic Diagram Symbols

• Resistor – Represents resistance in a circuit.
• Capacitor – Stores electrical energy temporarily.
• Inductor – Stores energy in a magnetic field when electrical current passes through it.
• Diode – Allows current to flow in one direction only.
• Light Emitting Diode (LED) – Emits light when current flows through it.
• Transistor (NPN and PNP) – Acts as a switch or amplifier.
• Battery – Provides a constant voltage supply.
• Ground – Represents a reference point in the circuit.
• Switch (SPST, SPDT) – Opens or closes a circuit.
• Relay – Electrically operated switch.
• Fuse – Protects the circuit by breaking the connection if the current is too high.
• Transformer – Transfers electrical energy between two or more circuits through electromagnetic induction.
• Op-Amp (Operational Amplifier) – Amplifies voltage signals.
• Voltage Source – Provides a constant voltage.
• Current Source – Provides a constant current.
• Potentiometer – Variable resistor used to adjust voltage or current.
• Connector (Male and Female) – Connects different circuit parts.
• Crystal Oscillator – Provides a stable clock signal for digital circuits.
• Antenna – Receives or transmits radio signals.
• Meter (Voltmeter, Ammeter) – Measures voltage, current, or resistance.
• Integrated Circuit (IC) – Represents complex circuits within a single chip.
• Junction (Wire Connection) – Shows where wires connect or do not connect.

Schematic Diagram Examples

• Simple LED Circuit: This basic schematic diagram shows the connection of a power source to an LED with a resistor in series to limit the current. The components include a battery, a resistor, and an LED, with lines indicating the connections. Components: Battery (Power Source), Resistor, LED
• Series and Parallel Circuit: This schematic represents a combination of series and parallel circuits. It includes two resistors in series connected to a power source, with another resistor connected in parallel to one of the series resistors. Components: Battery (Power Source), Resistors (R1, R2, R3)
• Transistor Switch Circuit: This schematic diagram shows a simple transistor switch. When the input signal is applied to the base of the transistor, it allows current to flow from the collector to the emitter, turning on an LED. Components: Power Source (Battery), Resistor (R1), Transistor (Q1), LED
• Operational Amplifier (Op-Amp) Inverting Amplifier: This schematic diagram illustrates an inverting amplifier using an operational amplifier. The input signal is fed through a resistor to the inverting input of the op-amp, with feedback provided by another resistor. Components: Operational Amplifier (Op-Amp), Resistors (R1, R2), Power Source (V+ and V-)
• Full-Wave Rectifier Circuit: This schematic diagram shows a full-wave rectifier using four diodes arranged in a bridge configuration. It converts an AC input to a DC output. Components: AC Power Source, Diodes (D1, D2, D3, D4), Load Resistor (R)
• 555 Timer Astable Multivibrator: This schematic diagram shows an astable multivibrator circuit using the 555 timer IC. This configuration generates a continuous square wave output. Components: 555 Timer IC, Resistors (R1, R2), Capacitor (C1), Power Source (Vcc), Ground
• Wheatstone Bridge: This schematic diagram illustrates a Wheatstone bridge, a circuit used to measure unknown resistance values by balancing two legs of a bridge circuit. Components: Resistors (R1, R2, R3, Rx), Galvanometer, Power Source (V)
• RC Low-Pass Filter: This schematic diagram represents an RC low-pass filter, which allows low-frequency signals to pass through while attenuating high-frequency signals. Components: Resistor (R), Capacitor (C), Input Signal (Vin), Output Signal (Vout)
• Voltage Divider: This schematic diagram shows a voltage divider circuit, which produces a fraction of the input voltage as its output. Components: Resistors (R1, R2), Input Voltage (Vin), Output Voltage (Vout)
• AND Gate: This schematic diagram represents a digital AND gate, which outputs a high signal only when both inputs are high. Components: Transistors (Q1, Q2), Resistors (R1, R2), Power Source (Vcc), Ground, Input Signals (A, B), Output Signal (Y)
• Full Adder Circuit: This schematic diagram shows a full adder circuit, which adds three binary digits and outputs a sum and a carry bit. Components: Logic Gates (AND, OR, XOR), Input Signals (A, B, Cin), Output Signals (Sum, Cout)

Schematic Diagram in Research

A schematic diagram in research is a visual tool that represents complex processes, structures, or systems in a simplified, abstract manner. It uses standardized symbols and lines to illustrate relationships and flows, making it easier to understand, communicate, and analyze intricate concepts.

Applications in Various Research Fields

• Electrical Engineering: Schematic diagrams show the layout of electrical circuits, highlighting connections between components like resistors, capacitors, and transistors.
• Mechanical Engineering: They represent the assembly and functioning of mechanical systems, such as engines or machinery, showing the relationship between different parts.
• Molecular Biology: Diagrams illustrate pathways of biochemical reactions, gene expression, and cellular processes.
• Ecology: Schematic representations are used to depict food webs, nutrient cycles, and energy flows within ecosystems.
• Psychology: Researchers use schematic diagrams to outline theoretical models, cognitive processes, and experimental designs.
• Sociology: Diagrams map out social structures, interactions, and network relationships.
• Anatomy: Schematic diagrams provide clear illustrations of anatomical structures and physiological processes.
• Pharmacology: They depict drug action mechanisms, metabolic pathways, and interactions within the body.

Schematic Diagram Types

Schematic diagrams come in various forms, each suited for different applications and levels of detail. Here are the primary types:

1. Block Diagrams

Block diagrams use simple geometric shapes to represent the different parts of a system and their interconnections. They provide a high-level overview of the system, illustrating the basic structure and functionality without delving into detailed component connections.

2. Circuit Diagrams

Circuit diagrams, also known as electrical schematics, depict the detailed connections between various electronic components. They use standardized symbols to represent elements such as resistors, capacitors, and transistors, making it easier to understand and troubleshoot electronic circuits.

3. Single-Line Diagrams

Single-line diagrams, or one-line diagrams, represent complex electrical systems in a simplified manner by using single lines to depict multiple connections. These diagrams are commonly used in power distribution systems to illustrate the flow of electricity.

4. Ladder Diagrams

Ladder diagrams are used in industrial control systems to represent the logic and sequence of operations. They resemble a ladder, with vertical lines representing power supply rails and horizontal lines representing control circuits.

5. Functional Flow Block Diagrams (FFBDs)

FFBDs illustrate the functional flow of a system or process, breaking it down into sequential steps. They are used in systems engineering to analyze and design complex systems by showing the interactions between different functions.

Difference between Schematic Diagrams and Wiring Diagrams

FAQ’s

Why are schematic diagrams used.

Schematic diagrams are used to simplify the understanding of complex systems, providing a clear visual of components and their interactions.

Where are schematic diagrams commonly used?

They are commonly used in electronics, engineering, architecture, and manufacturing to plan and troubleshoot systems.

What are the basic elements of a schematic diagram?

The basic elements include symbols representing components and lines indicating connections between them.

How do you read a schematic diagram?

Start by identifying the symbols and their meanings, then follow the connections between components to understand the system flow.

What is the difference between a schematic diagram and a circuit diagram?

A schematic diagram focuses on the functionality and connections, while a circuit diagram shows the physical layout of components.

Can schematic diagrams vary in complexity?

Yes, they can range from simple diagrams for basic systems to highly complex ones for intricate designs.

What symbols are used in schematic diagrams?

Common symbols include resistors, capacitors, transistors, and diodes, among others.

How are connections represented in schematic diagrams?

Connections are typically represented by lines that may have various styles, such as solid or dashed, indicating different types of connections.

What software is used to create schematic diagrams?

Software like AutoCAD, Eagle, and Microsoft Visio are popular for creating schematic diagrams.

How important is accuracy in schematic diagrams?

Accuracy is crucial as errors can lead to misunderstandings and malfunctions in the actual system.

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Trump assassination attempt: Graphics, maps show you what happened

Corrections and clarifications: An earlier version of this story misstated the approximate distance between the rooftop and the stage. The distance is about 150 yards. The approximate location of the shooter's body has also been updated in the graphics .

An investigation continues into the attempted assassination of former President Donald Trump at a rally in Bulter, Pennsylvania, on Saturday, in which one attendee was shot and killed and two others seriously injured.

The gunman was shot and killed by Secret Service agents. The FBI later identified him as Thomas Matthew Crooks , 20, of Bethel Park, Pennsylvania, about 40 miles south of Butler. His motive is not yet known.

Details continue to emerge. Trump says a bullet pierced the upper part of his right ear before Secret Service agents hustled him off the stage and into a limousine. He was reported to be otherwise unharmed.

The gunman, who is believed to have acted alone, fired at the rally stage from a building rooftop about 150 yards away, outside the rally's security perimeter. Agents recovered an AR-style rifle from the scene.

Here is what we know at the moment. All times are Eastern:

Where was Trump?

1 p.m.: The Butler Farm Show, site of the rally, opens its doors to attendees. Trump is scheduled to speak at 5 p.m.

6:03 p.m.: Trump takes the stage and greets the crowd as the Lee Greenwood song “God Bless the USA” plays.

6:05 p.m.:  The song ends, and Trump begins speaking.

Unable to view our graphics? Click here to see them.

6:11 p.m.: While Trump is speaking, multiple shots are fired toward the stage. Videos show Trump grabbing his right ear, looking at his bloody hand and dropping to the ground behind the podium. People can be heard saying, "Shots, shots, shots."

6:12 p.m.: Secret Service agents jump on top of Trump and escort him off stage and into a vehicle. Trump gives a thumbs up as he leaves.

How many shots were fired?

6:14 p.m.: Trump's motorcade leaves the fairgrounds surrounded by law enforcement vehicles.

6:42 p.m.: The Secret Service  issues a statement confirming “an incident”  took place at the rally and that Trump “is safe.” Shortly after, the Trump campaign issues a statement saying Trump “is fine and is being checked out at a local medical facility."

7:24 p.m.: The Butler County district attorney says the suspected shooter is dead and one rally attendee has been killed, the Associated Press reports.

Where was the shooter?

7:49 p.m.: Secret Service spokesman Anthony Guglielmi  releases a statement  saying agents neutralized the shooter and that he was dead. The statement says one person was killed and two spectators have been seriously injured.

8:13 p.m.: In a short televised briefing, President Joe Biden says he was trying to call Trump  to speak with him as soon as possible.

8:42 p.m.: Trump posts on Truth Social confirming he was shot :

• “It is incredible that such an act can take place in our Country. Nothing is known at this time about the shooter, who is now dead. I was shot with a bullet that pierced the upper part of my right ear. I knew immediately that something was wrong in that I heard a whizzing sound, shots, and immediately felt the bullet ripping through the skin. Much bleeding took place, so I realized then what was happening. GOD BLESS AMERICA!"

9:33 p.m.: The FBI's Pittsburgh office says it has assumed the lead in the shooting investigation.

11:52 p.m.: In a news conference, Kevin Rojek, special agent in charge of the Pittsburgh FBI office, says the shooting was an attempted assassination of Trump and that investigators are working to determine a motive.

Who shot Trump? What gun was used?

Sunday: Law enforcement sealed off the home of Thomas Matthew Crooks for investigation.

Crooks used a legally-purchased "AR-style 556 rifle," said Kevin Rojek, a special agent in charge of the FBI's Pittsburgh field office, on a call with reporters. The agent likely refers to a rifle that fires 5.56 mm ammunition, though there are some firearm models with "556" in their name.

The weapon was located next to Crooks on the scene, Rojek said.

Rojek said law enforcement located "a suspicious device" when they searched the Crooks' vehicle. The device is being analyzed at the FBI crime lab in Quantico, Virginia.

Agents also obtained a court order to examine Crooks' cellphone in hopes its contents will provide clues into the shooting.

"At this time, the information that we have indicates that the shooter acted alone and that there are currently no public safety concerns," Rojek said. Another unidentified official on the call said the FBI believes the weapon was bought by the shooter's father. The family is cooperating with the investigation, officials said.

More coverage:

Trump rally shooting victims: Pennsylvania firefighter killed, 2 local residents wounded

Read more : Trump rally shooter Thomas Crooks appears to have acted alone, used 'AR-style 556' rifle: FBI

Nursing aide turned sniper : Thomas Crooks' mysterious plot to kill Trump

CONTRIBUTING Natalie Neysa Alund and Aysha Bagchi, USA TODAY.

SOURCE USA TODAY Network reporting and research; Reuters