data representation and interpretation grade 11

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DATA REPRESENTATION AND PREDICTION (Daththa Nirupanaya Ha Arthakathanaya) | Grade 11 Maths Textbook Answers

Grade 11 Maths Textbook Answers Lesson 15 - DATA REPRESENTATION AND PREDICTION (Daththa Nirupanaya Ha Arthakathanaya)

Download Grade 11 Maths textbook answers for DATA REPRESENTATION AND PREDICTION (Daththa Nirupanaya Ha Arthakathanaya), Lesson 15 in Sinhala Medium. DATA REPRESENTATION AND PREDICTION (Daththa Nirupanaya Ha Arthakathanaya) Answers are available in PDF format. Download using the Link Below. It’s free to download.

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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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Data Analysis Class 11 Notes

Teachers and Examiners ( CBSESkillEduction ) collaborated to create the Data Analysis Class 11 Notes . All the important Information are taken from the NCERT Textbook Artificial Intelligence (417) .

Structured Data

Structured data is a standardized format for describing a page’s content and categorizing it. for example, Names, dates, addresses, credit card numbers, stock data, and other everyday items.

It is a clear structure, and is highly organized in a structured repository. In a relational database management system, it can be simply stored and found because it neatly fits into fixed fields and columns (RDBMS).

Common sources of structured data are: a. Excel files b. SQL databases c. Medical devices Logs d. Online Forms

Characteristics of Structured Data a. High organized b. Clearly defined c. Easy to access d. Easy to analyze

Examples of Structured Data a. Name b. Age c. Gender d. Address e. Phone Number f. Currency g. Date h. Billing info

Sources of Structured Data a. SQL database b. Spreadsheet c. Sensors d. Medical Device e. Online Forms f. Point of Sales Systems g. Web and Server Logs

Date and Time Datatype

Date and Time datatypes are used to hold values with both date and time information. Date-time information can be stored in a variety of formats.

String Data Type

An array of bytes (or words) that stores a succession of elements is frequently used to build the structured data type known as a string. A string can contain [A – Z], [as z], [0 -9], and [all special characters], yet they are all treated as though they were text because they can store alphanumeric data. There are also spaces in it. String information has to be enclosed in quotes (“”or”).

Examples: Address = “9th Floor, SAS Tower, Gurgaon” “Hamburger” “I ate 3 hamburgers”.

Categorical Data Types

The term “categorical data” also refers to a collection of information that may be categorised into categories, such as the report cards for all students. Because it may be categorised based on the variables included in the report card, such as class, subjects, sections, school-house, etc., this data is known as categorical data.

There are four different type of Categorical Data Type – a. Nominal b. Continuous c. Ordinal d. Binary

Representation of Data

The study of statistics focuses on gathering, organizing, analyzing, interpreting, and presenting data. The observations are turned into useful knowledge via data science. To complete this work, statisticians condense a lot of data into a format that is manageable and yields useful information.

Data representation techniques are broadly classified in two ways –

Non-Graphical technique – Tabular form and case form Large datasets should not be represented in this outdated format. When our goal is to make decisions after analysing a set of data, non-graphical techniques are less suitable.

Graphical Technique – Pie Chart, Bar graphs, line graphs, etc. The most typical visual representation of statistical data is in the form of points, lines, dots, and other geometric shapes. Due to time restrictions, it would not be feasible to describe the creation techniques for all sorts of diagrams and maps.

for example – a. Line graphs b. Bar diagrams c. Pie diagram d. Scatter Plots

Line Graphs

A line graph, often known as a line chart, is a visual representation of data that is constantly changing over time. A line graph connects the data using points that display a continuous change. Depending on the data points they represent, the lines in a line graph can either ascend or drop.

The advantages of using Line graph is that it is useful for making comparisons between different datasets, it is easy to tell the changes in both long and short term, with even small changes over time.

Bar Diagram

The bars in a bar graph, commonly referred to as a bar chart or bar diagram, are used to compare data between categories. The bar’s length is inversely proportional to the value it stands for. Simply put, the value a bar represents increases with length. The graph’s bars, which can run either horizontally or vertically, are all the same width.

Following rules should be observed while constructing a bar diagram: (a) The width of all the bars or columns should be similar. (b) All the bars should be placed on equal intervals/distance. (c) Bars may be shared with colours or patterns to make them distinct and attractive.

Bar Diagram helpful for comparing data, offer a visual representation for quick comparison of amounts in various categories, and make determining relationships simple. Large changes over time are also depicted in bar graphs.

A circular graph with numerous parts or sections is known as a pie chart. Each sector (segment) of the pie represents the relative size, i.e., the percentage or contribution that each category made to the overall pie. Each part of the diagram resembles a slice of a pie, and the whole thing looks like one. Data from a short table can often be visualised using pie charts.

The advantages of a pie chart is that it is simple and easy-to-understand and provides data comparison at a glance.

Scatter Plots

Scatter plots are used to show the relationship between two variables (or aspects) for a collection of paired data. They consist of a set of data points plotted along the x and y axes. The various shapes that the data points take tell a tale all their own, most frequently indicating the connection (positive or negative) in a lot of data.

Types of Correlation

The statistical concept of correlation describes how closely two variables move in parallel with one another. Two variables are considered to have a positive correlation if they move in the same direction. They have a negative correlation if they travel in the opposite directions.

Positive Correlation – Both variables are seen to be moving in the same direction. In other words, with the increase in one variable, the other variable also increases.

Negative Correlation – Both the variables are seen to be moving in opposite directions. While one variable increases, the other variable decreases.

Exploring Data

Exploring data entails “getting to know” the data, including its values and their typical, unusual, focused, or extreme characteristics. More significantly, throughout the exploration process, one has the chance to spot and fix any issues with their data that could perhaps influence the findings they come to during analysis. This is the first step in data analysis and involves summarizing the main characteristics of a dataset, such as its size, accuracy, initial patterns in the data and other attributes.

Case, Variables and Levels of Measurement

Cases and variables.

A variable is a quality that may be measured and have several values. Or, anything that varies depending on the circumstance. In contrast, a constant in a research study is the same in every situation. Case a sampling point for an experimental unit.

Cases are nothing more than a collection of objects, a dataset is said to consist of cases.

Levels of Measurement

The level of measurement refers to the method used to determine a set of data. Data cannot be treated equally in all cases. It makes logical to categorise data sets using several standards. Some are qualitative while others are quantitative. There are discrete and continuous data sets. The type of qualitative data can be nominal or ordinal. Additionally, interval and ratio data can be separated into two types.

Nominal Level

Nominal-level data are qualitative data. The four seasons of winter, spring, summer, and autumn are examples of nominal variables, as are product categories like Mercedes, BMW, or Audi. Since they are not numbers, they cannot be ranked or utilised in calculations. The easiest or lowest of the four ways to characterise data is the nominal level of measurement.

Ordinal Level

Ordinal data is composed of groups and categories that are arranged in a specific order. For instance, suppose you were asked to give a restaurant meal a rating and you had the choice between unpleasant, unappetizing, just acceptable, tasty, and delicious. Although the restaurant utilised words rather than numbers to judge the quality of its meals, it is obvious that these preferences are ranked from low to high or from negative to positive, making the data qualitative rather than ordinal. The disparity between the data, however, cannot be quantified. Ordinal scale data cannot be used in calculations, much like nominal scale data.

Interval Level

Because it has a clear ordering, data measured using the interval scale is similar to data recorded using the ordinal scale, but there are some differences as well. Even though the data does not have a starting point, or a zero value, the differences between interval scale data can still be measured.

Ratio Scale Level

Similar to interval scale data, ratio scale data has a 0 point and can be used to calculate ratios. For instance, the results of four multiple-choice questions on the final test in statistics were 80, 68, 20, and 92 (out of a possible 100). The grades are produced by a computer. The numbers 20, 68, 80, and 92 can be arranged from lowest to highest, or vice versa. The variations in the data are significant. The score 92 is 24 points higher than the score 68. One can compute ratios. The lowest score is zero. 20 divided by 4 equals 80. An 80 is four times better than a 20, for example.

Data Matrix and Frequency Tables

What is data matrix.

The Data Matrix is a tabular representation of the cases and variables utilised in your statistical analysis. In a data matrix, each row denotes a case and each column a variable. There could be hundreds, lakhs, or even more examples in a complete data matrix.

Frequency Tables

The number of times a specific data value happens (occurrences) in a given set of data is the frequency of that data value. In cricket, if four players each score 90 runs, the score of 90 is said to occur four times. ‘f’ is frequently used to denote a data value’s frequency.

Graphs and Shapes of Distributions

Statisticians or machine learning engineers often want to summarize the data they have. They can do it by various available methods like data matrix, frequency tables or by graphical representation. When graphed, the data in a set is arranged to show how the points are distributed throughout the set.

Mean, Median and Mode

Imagine yourself returning home with your report card after the announcement of your final grades in class. Your parents will ask, “What is your average score?” regarding your grades and general performance. In actuality, they’re looking for your MEAN score.

The most often used and well-known index of central tendency is the mean (or average). The mean is determined by dividing the total number of values in the data set by the number of values in the data set. The mean in this situation is calculated by adding up all of your marks and dividing them by the number of topics.

M = ∑ fox / n Where M = Mean ∑ = Sum total of the scores f = Frequency of the distribution x = Scores n = Total number of cases

The value of an observation for which half are larger and half are smaller is known as the median. The mean of the two middle points is calculated if the number of data points is even. For the median difference, the median for two samples is calculated, and then their difference is calculated.

For a grouped data, calculation of a median in continuous series involves the following steps: (I) The data arranged in ascending order of their class interval (ii) Frequencies are converted into cumulative frequencies (iii) Median class of the series is identified (iv) Formula used to find actual median value

Another crucial indicator of a tactical series’ primary tendency is its mode. In the data series, it is the value that appears the most frequently. The most frequent score in our data set is the mode. It stands in for the highest bar on a histogram or bar chart. Therefore, you might occasionally think of the mode as the most common choice.

Z – score (For Advance Learners)

The Z-score provides us with a notion of how far our particular data point is from the mean. Technically speaking, it’s a measurement of how far the data point deviates from the population mean by standard deviations. If a value is above the mean, the z-score is positive; if it is below the mean, it is negative.

How do we interpret a z-score?

The value of the z-score tells you how many standard deviations your data point is away from the mean. If a zscore is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean. A negative z-score reveals the raw score is below the mean average. For example, if a z-score is equal to -2.

Employability Skills Class 11 Notes

• Unit 1 : Communication Skills – III
• Unit 2 : Self-Management Skills – III
• Unit 3 : Information and Communication Technology Skills – III
• Unit 4 : Entrepreneurial Skills – III
• Unit 5 : Green Skills – III

Employability Skills Class 11 MCQ

Employability skills class 11 questions and answers, subject specific skills notes.

• Unit 1: Introduction To AI
• Unit 2: AI Applications & Methodologie
• Unit 3: Maths For AI
• Unit 4: AI Values (Ethical Decision Making)
• Unit 5: Introduction To Storytelling
• Unit 6: Critical & Creative Thinking
• Unit 7: Data Analysis (Computational Thinking)
• Unit 8: Regression
• Unit 9: Classification & Clustering
• Unit 10: AI Values (Bias Awareness)

Free Printable data visualization Worksheets for 11th Grade

Math data visualization made accessible! Discover a collection of free printable worksheets for Grade 11 students, designed to enhance their understanding of complex mathematical concepts through visually appealing representations. Empower your teaching with Quizizz!

11th - 12th

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Explore printable data visualization worksheets for 11th Grade

Data visualization worksheets for Grade 11 are an essential resource for teachers looking to enhance their students' understanding of Math, probability, and statistics. These worksheets provide a visual representation of complex data sets, allowing students to easily comprehend and analyze the information presented. By incorporating these worksheets into their lesson plans, teachers can effectively engage their students and help them develop critical thinking skills. Additionally, these worksheets can be used to reinforce concepts taught in class, providing students with ample opportunities to practice and improve their skills. With a variety of topics covered, such as bar graphs, pie charts, and scatter plots, data visualization worksheets for Grade 11 are an invaluable tool for any teacher looking to elevate their Math, probability, and statistics curriculum.

Quizizz is an excellent platform for teachers to access data visualization worksheets for Grade 11, along with a plethora of other resources. This interactive platform offers a wide range of quizzes, games, and activities that can be easily integrated into lesson plans, making learning Math, probability, and statistics more engaging and enjoyable for students. Teachers can also create their own quizzes and worksheets, tailoring the content to suit their students' needs and learning objectives. Furthermore, Quizizz provides real-time feedback and analytics, allowing teachers to monitor their students' progress and identify areas that may require additional support or instruction. By utilizing Quizizz in conjunction with data visualization worksheets for Grade 11, teachers can create a comprehensive and dynamic learning experience that will undoubtedly benefit their students.

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Represent and Interpret Data Facts & Worksheets

In this lesson, we will try to understand scaled picture graphs and bar graphs in order to represent a data set with several categories., search for worksheets, download the represent and interpret data facts & worksheets.

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Table of Contents

In this lesson, we will try to understand scaled picture graphs and bar graphs in order to represent a data set with several categories. Aside from that, we will also be measuring lengths using rulers marked with halves and fourths of an inch.

See the fact file below for more information on the representation and interpretation data or alternatively, you can download our 34-page Represent and Interpret Data worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

• A type of graph that displays data using pictures and symbols.
• A type of graph that displays data that visually allows for quick and easy conclusions. This can either be vertical (bottom to top) or horizontal (left to right) bars whose lengths represent amounts or numbers.
• The part of a map or graph that explains the symbols.

PICTURE GRAPHS

• Example 1. Elizabeth sold cookies last summer . She made a picture graph to show how many cookies she sold on her first day. She made a table. How can you display the data in a picture graph?
• A bar graph uses bars to show data. A scale of equally spaced numbers helps you read the numbers each bar shows.
• A bar graph needs the following labels: (1) title, (2) categories, (3) category label, (4) number interval, and (5) number interval label.
• In a horizontal bar graph, the bars go across from left to right. The length of the bar shows the number.
• In a vertical bar graph, the bars go up from the bottom. The height of the bar represents the number.

MEASURING HALVES AND FOURTHS OF AN INCH

• By now, you have an idea that that measurements are not always exact to a whole unit.

UNDERSTANDING MEASUREMENTS

• We have already established the understanding that not all measurements are exact. Now, we will try to establish an understanding of how some measurements, despite measuring the same object, are different.

LINE PLOTS: DISPLAYING DATA

• Now, we will try to display data in a line plot. To do this, we will use a number line to represent the measurements in whole numbers, halves, and fourths.

Represent and Interpret Data Worksheets

This is a fantastic bundle which includes everything you need to know about the representation and interpretation of data across 34 in-depth pages. These are ready-to-use Represent and Interpret Data worksheets that are perfect for teaching students about the scaled picture graphs and bar graphs in order to represent a data set with several categories. Aside from that, we will also be measuring lengths using rulers marked with halves and fourths of an inch.

Complete List Of Included Worksheets

• Lesson Plan
• Represent and Interpret Data
• Measure It!
• Compare the Length
• Worms For Breakfast
• Trip to the Zoo
• Say Cheeze!
• Summer Camping
• Which Sport
• Breakfast Faves
• Your Own Plot

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