graphical representation wikipedia

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Graphical Representation of Data

Graphical Representation of Data: Graphical Representation of Data,” where numbers and facts become lively pictures and colorful diagrams . Instead of staring at boring lists of numbers, we use fun charts, cool graphs, and interesting visuals to understand information better. In this exciting concept of data visualization, we’ll learn about different kinds of graphs, charts, and pictures that help us see patterns and stories hidden in data.

There is an entire branch in mathematics dedicated to dealing with collecting, analyzing, interpreting, and presenting numerical data in visual form in such a way that it becomes easy to understand and the data becomes easy to compare as well, the branch is known as Statistics .

The branch is widely spread and has a plethora of real-life applications such as Business Analytics, demography, Astro statistics, and so on . In this article, we have provided everything about the graphical representation of data, including its types, rules, advantages, etc.

Table of Content

What is Graphical Representation

Types of graphical representations, line graphs, histograms , stem and leaf plot , box and whisker plot .

• Graphical Representations used in Maths

Value-Based or Time Series Graphs 

Frequency based, principles of graphical representations, advantages and disadvantages of using graphical system, general rules for graphical representation of data, frequency polygon, solved examples on graphical representation of data.

Graphics Representation is a way of representing any data in picturized form . It helps a reader to understand the large set of data very easily as it gives us various data patterns in visualized form.

There are two ways of representing data,

• Pictorial Representation through graphs.

They say, “A picture is worth a thousand words”.  It’s always better to represent data in a graphical format. Even in Practical Evidence and Surveys, scientists have found that the restoration and understanding of any information is better when it is available in the form of visuals as Human beings process data better in visual form than any other form.

Does it increase the ability 2 times or 3 times? The answer is it increases the Power of understanding 60,000 times for a normal Human being, the fact is amusing and true at the same time.

Check: Graph and its representations

Comparison between different items is best shown with graphs, it becomes easier to compare the crux of the data about different items. Let’s look at all the different types of graphical representations briefly: 

A line graph is used to show how the value of a particular variable changes with time. We plot this graph by connecting the points at different values of the variable. It can be useful for analyzing the trends in the data and predicting further trends. 

A bar graph is a type of graphical representation of the data in which bars of uniform width are drawn with equal spacing between them on one axis (x-axis usually), depicting the variable. The values of the variables are represented by the height of the bars. 

This is similar to bar graphs, but it is based frequency of numerical values rather than their actual values. The data is organized into intervals and the bars represent the frequency of the values in that range. That is, it counts how many values of the data lie in a particular range. 

It is a plot that displays data as points and checkmarks above a number line, showing the frequency of the point.  

This is a type of plot in which each value is split into a “leaf”(in most cases, it is the last digit) and “stem”(the other remaining digits). For example: the number 42 is split into leaf (2) and stem (4).  

These plots divide the data into four parts to show their summary. They are more concerned about the spread, average, and median of the data. 

It is a type of graph which represents the data in form of a circular graph. The circle is divided such that each portion represents a proportion of the whole. 

Graphical Representations used in Math’s

Graphs in Math are used to study the relationships between two or more variables that are changing. Statistical data can be summarized in a better way using graphs. There are basically two lines of thoughts of making graphs in maths: 

• Value-Based or Time Series Graphs

These graphs allow us to study the change of a variable with respect to another variable within a given interval of time. The variables can be anything. Time Series graphs study the change of variable with time. They study the trends, periodic behavior, and patterns in the series. We are more concerned with the values of the variables here rather than the frequency of those values. 

Example: Line Graph

These kinds of graphs are more concerned with the distribution of data. How many values lie between a particular range of the variables, and which range has the maximum frequency of the values. They are used to judge a spread and average and sometimes median of a variable under study.

Also read: Types of Statistical Data

• All types of graphical representations follow algebraic principles.
• When plotting a graph, there’s an origin and two axes.
• The x-axis is horizontal, and the y-axis is vertical.
• The axes divide the plane into four quadrants.
• The origin is where the axes intersect.
• Positive x-values are to the right of the origin; negative x-values are to the left.
• Positive y-values are above the x-axis; negative y-values are below.

• It gives us a summary of the data which is easier to look at and analyze.
• It saves time.
• We can compare and study more than one variable at a time.

Disadvantages

• It usually takes only one aspect of the data and ignores the other. For example, A bar graph does not represent the mean, median, and other statistics of the data. 
• Interpretation of graphs can vary based on individual perspectives, leading to subjective conclusions.
• Poorly constructed or misleading visuals can distort data interpretation and lead to incorrect conclusions.

Check : Diagrammatic and Graphic Presentation of Data

We should keep in mind some things while plotting and designing these graphs. The goal should be a better and clear picture of the data. Following things should be kept in mind while plotting the above graphs: 

• Whenever possible, the data source must be mentioned for the viewer.
• Always choose the proper colors and font sizes. They should be chosen to keep in mind that the graphs should look neat.
• The measurement Unit should be mentioned in the top right corner of the graph.
• The proper scale should be chosen while making the graph, it should be chosen such that the graph looks accurate.
• Last but not the least, a suitable title should be chosen.

A frequency polygon is a graph that is constructed by joining the midpoint of the intervals. The height of the interval or the bin represents the frequency of the values that lie in that interval. 

Question 1: What are different types of frequency-based plots? 

Types of frequency-based plots:  Histogram Frequency Polygon Box Plots

Question 2: A company with an advertising budget of Rs 10,00,00,000 has planned the following expenditure in the different advertising channels such as TV Advertisement, Radio, Facebook, Instagram, and Printed media. The table represents the money spent on different channels. 

Draw a bar graph for the following data. 

• Put each of the channels on the x-axis
• The height of the bars is decided by the value of each channel.

Question 3: Draw a line plot for the following data 

• Put each of the x-axis row value on the x-axis
• joint the value corresponding to the each value of the x-axis.

Question 4: Make a frequency plot of the following data: 

• Draw the class intervals on the x-axis and frequencies on the y-axis.
• Calculate the midpoint of each class interval.

Now join the mid points of the intervals and their corresponding frequencies on the graph. 

This graph shows both the histogram and frequency polygon for the given distribution.

Related Article:

Graphical Representation of Data| Practical Work in Geography Class 12 What are the different ways of Data Representation What are the different ways of Data Representation? Charts and Graphs for Data Visualization

Conclusion of Graphical Representation

Graphical representation is a powerful tool for understanding data, but it’s essential to be aware of its limitations. While graphs and charts can make information easier to grasp, they can also be subjective, complex, and potentially misleading . By using graphical representations wisely and critically, we can extract valuable insights from data, empowering us to make informed decisions with confidence.

Graphical Representation of Data – FAQs

What are the advantages of using graphs to represent data.

Graphs offer visualization, clarity, and easy comparison of data, aiding in outlier identification and predictive analysis.

What are the common types of graphs used for data representation?

Common graph types include bar, line, pie, histogram, and scatter plots , each suited for different data representations and analysis purposes.

How do you choose the most appropriate type of graph for your data?

Select a graph type based on data type, analysis objective, and audience familiarity to effectively convey information and insights.

How do you create effective labels and titles for graphs?

Use descriptive titles, clear axis labels with units, and legends to ensure the graph communicates information clearly and concisely.

How do you interpret graphs to extract meaningful insights from data?

Interpret graphs by examining trends, identifying outliers, comparing data across categories, and considering the broader context to draw meaningful insights and conclusions.

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This is a collection of our favorite visualizations, infographics, and other projects built on open data from Wikipedia and other Wikimedia projects, curated by Stephen LaPorte and Mahmoud Hashemi . Source code and more details about this page are available on Github .

If you know other cool Wikipedia-based projects, please submit a link .

Not all of the projects have their source code or data posted online. If you have more information about any of these porjects, please get in touch . We'd love to hear more.

Check out more Wikipedia data , too.

Further reading

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Data Visualization: Definition, Benefits, and Examples

Data visualization helps data professionals tell a story with data. Here’s a definitive guide to data visualization.

Data visualization is a powerful way for people, especially data professionals, to display data so that it can be interpreted easily. It helps tell a story with data, by turning spreadsheets of numbers into stunning graphs and charts.

In this article, you’ll learn all about data visualization, including its definition, benefits, examples, types, and tools. If you decide you want to learn the skills to incorporate it into your job, we'll point you toward online courses you can do from anywhere.

What is data visualization?

Data visualization is the representation of information and data using charts, graphs, maps, and other visual tools. These visualizations allow us to easily understand any patterns, trends, or outliers in a data set.

Data visualization also presents data to the general public or specific audiences without technical knowledge in an accessible manner. For example, the health agency in a government might provide a map of vaccinated regions.

The purpose of data visualization is to help drive informed decision-making and to add colorful meaning to an otherwise bland database.

Benefits of data visualization

Data visualization can be used in many contexts in nearly every field, like public policy, finance, marketing, retail, education, sports, history, and more. Here are the benefits of data visualization:

Storytelling: People are drawn to colors and patterns in clothing, arts and culture, architecture, and more. Data is no different—colors and patterns allow us to visualize the story within the data.

Accessibility: Information is shared in an accessible, easy-to-understand manner for a variety of audiences.

Visualize relationships: It’s easier to spot the relationships and patterns within a data set when the information is presented in a graph or chart.

Exploration: More accessible data means more opportunities to explore, collaborate, and inform actionable decisions.

Data visualization and big data

Companies collect “ big data ” and synthesize it into information. Data visualization helps portray significant insights—like a heat map to illustrate regions where individuals search for mental health assistance. To synthesize all that data, visualization software can be used in conjunction with data collecting software.

Tools for visualizing data

There are plenty of data visualization tools out there to suit your needs. Before committing to one, consider researching whether you need an open-source site or could simply create a graph using Excel or Google Charts. The following are common data visualization tools that could suit your needs. 

Google Charts

ChartBlocks

FusionCharts

Get started with a free tool

No matter the field, using visual representations to illustrate data can be immensely powerful. Tableau has a free public tool that anyone can use to create stunning visualizations for a school project, non-profit, or small business. 

Types of data visualization

Visualizing data can be as simple as a bar graph or scatter plot but becomes powerful when analyzing, for example, the median age of the United States Congress vis-a-vis the median age of Americans . Here are some common types of data visualizations:

Table: A table is data displayed in rows and columns, which can be easily created in a Word document or Excel spreadsheet.

Chart or graph: Information is presented in tabular form with data displayed along an x and y axis, usually with bars, points, or lines, to represent data in comparison. An infographic is a special type of chart that combines visuals and words to illustrate the data.

Gantt chart: A Gantt chart is a bar chart that portrays a timeline and tasks specifically used in project management.

Pie chart: A pie chart divides data into percentages featured in “slices” of a pie, all adding up to 100%. 

Geospatial visualization: Data is depicted in map form with shapes and colors that illustrate the relationship between specific locations, such as a choropleth or heat map.

Dashboard: Data and visualizations are displayed, usually for business purposes, to help analysts understand and present data.

Data visualization examples

Using data visualization tools, different types of charts and graphs can be created to illustrate important data. These are a few examples of data visualization in the real world:

Data science: Data scientists and researchers have access to libraries using programming languages or tools such as Python or R, which they use to understand and identify patterns in data sets. Tools help these data professionals work more efficiently by coding research with colors, plots, lines, and shapes.

Marketing: Tracking data such as web traffic and social media analytics can help marketers analyze how customers find their products and whether they are early adopters or more of a laggard buyer. Charts and graphs can synthesize data for marketers and stakeholders to better understand these trends. 

Finance: Investors and advisors focused on buying and selling stocks, bonds, dividends, and other commodities will analyze the movement of prices over time to determine which are worth purchasing for short- or long-term periods. Line graphs help financial analysts visualize this data, toggling between months, years, and even decades.

Health policy: Policymakers can use choropleth maps, which are divided by geographical area (nations, states, continents) by colors. They can, for example, use these maps to demonstrate the mortality rates of cancer or ebola in different parts of the world.  

Tackle big business decisions by backing them up with data analytics. Google's Data Analytics Professional Certificate can boost your skills:

Jobs that use data visualization

From marketing to data analytics, data visualization is a skill that can be beneficial to many industries. Building your skills in data visualization can help in the following jobs:

Data visualization analyst: As a data visualization analyst (or specialist), you’d be responsible for creating and editing visual content such as maps, charts, and infographics from large data sets. 

Data visualization engineer: Data visualization engineers and developers are experts in both maneuvering data with SQL, as well as assisting product teams in creating user-friendly dashboards that enable storytelling.

Data analyst: A data analyst collects, cleans, and interprets data sets to answer questions or solve business problems.

Data is everywhere. In creative roles such as graphic designer , content strategist, or social media specialist, data visualization expertise can help you solve challenging problems. You could create dashboards to track analytics as an email marketer or make infographics as a communications designer.

On the flip side, data professionals can benefit from data visualization skills to tell more impactful stories through data.

Read more: 5 Data Visualization Jobs (+ Ways to Build Your Skills Now)

Dive into data visualization

Learn the basics of data visualization with the University of California Davis’ Data Visualization with Tableau Specialization . You’ll leverage Tableau’s library of resources to learn best practices for data visualization and storytelling, learning from real-world and journalistic examples. Tableau is one of the most respected and accessible data visualization tools. 

To learn more about data visualization using Excel and Cognos Analytics, take a look at IBM’s Data Analysis and Visualization Foundations Specialization .

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What is a graph?

Representation of graphs, breadth-first search, depth-first search, contrasting traversals, additional problems.

Consider the highway system of the eastern coast of the United States. A road inspector is given the task of writing reports about the current condition of each highway. What would be the most economical way for him to traverse all the cities? The problem can be modeled as a graph.

In fact, since graphs are dots and lines , they look like road maps. The dots are called vertices or nodes and the lines are called edges. They may have a value assigned to them (weighted) or they may just be a mere indicator of the existence of a path (unweighted). More formally, a graph can be defined as follows:

A graph \(G\) consists of a set of \(V\) of vertices (or nodes ) and a set \(E\) of edges (or arcs ) such that each edge \(e \in E\) is associated with a pair of vertices \(\in V\). A graph \(G\) with vertices \(V\) and edges \(E\) is written as \(G=(V,E)\).

Because graphs are so pervasive, it is useful to define different types of graphs. The following are the most common types of graphs:

Undirected graph: An undirected graph is one in which its edges have no orientations, i.e. no direction is associated with any edge. The edges \((x,y)\) and \((y,x)\) are equivalent.

Directed graph: A directed graph or digraph \(G\) consists of a set \(V\) of vertices (or nodes) and a set of edges (or arcs) such that each edge \(e \in E\) is associated with an ordered pair of vertices. If there is an edge \((x,y)\), it is completely distinct from the edge \((y,x)\).

Undirected graphs are typically represented by a line with no arrows, which implies a bidirectional relationship between node A and node B. Directed graphs use an arrow to show the relationship from A to B.

Directed acyclic graph : A directed acyclic graph (commonly abbreviated as DAG) is a directed graph with no directed cycles. A cycle is any path \(\{A_1, \ldots, A_n\}\) such that the edges \(A_1\rightarrow A_2\), \(A_2\rightarrow A_3\), \(\ldots\), and \(A_n\rightarrow A_1\) all exist, thus forming a loop. A DAG is a graph without a single cycle.

List all the edges and vertices of the undirected graph \(G\) in the figure above. The graph \(G\) consists of the set of vertices \(V\) = {Massachusetts, Maine, Connecticut, New York, Maryland, New Jersey}. Its edges are \(E =\) {(Maine,Massachusetts) , (Massachusetts, Connecticut) , (Connecticut,New York), (New York,Maine), (New York,Massachusetts), (New Jersey, Maine),(Maryland, New York), (Maine, Maryland)}. Note that since the graph is undirected, the order of the tuples in denoting the edges is unimportant. \(_\square\)

Government surveillance agencies have a tendency to accumulate strange new powers during times of panic. The US National Security Agency (NSA) now has the ability to monitor the communications of suspected individuals as well as the communications of people within some number of hops of any suspect. In the communication network above, which person is connected to the greatest number of people through 1 hop or less?

Details and Assumptions:

• Each dot represents a person.
• Each line represents communication between the people on either end.
• If X communicates with Y, and Y communicates with Z, we say that X and Z have a 1-hop connection, and that X has a 0-hop connection with Y.

Above we represented a graph by drawing it. To represent it in a computer, however, we need more formal ways of representing graphs. Here we discuss the two most common ways of representing a graph: the adjacency matrix and the adjacency list.

The adjacency matrix

Represent the graph above using an adjacency matrix. To obtain the adjacency matrix of the graph, we first label the rows and columns with the corresponding ordered vertices. If there exists an edge between two vertices \(i\) and \(j\), then their corresponding cell in the matrix will be assigned \(1\). If there does not exist an edge, then the cell will be assigned the value \(0\). The adjacency matrix for the graph above is thus \[\quad \begin{bmatrix} & a & b & c & d & e\\ a & 0 & 1 & 1 & 0 & 1 \\ b & 1 & 0 & 0 & 0 & 0\\ c & 1 & 0 & 0 & 1 & 1\\ d & 0 & 0 & 1 & 0 & 0\\ e & 1 & 0 & 1 & 0 & 0\\ \end{bmatrix}. \ _\square \quad\]

Adjacency list

An adjacency list representation of a graph is a way of associating each vertex (or node) in the graph with its respective list of neighboring vertices. A common way to do this is to create a Hash table . This table will contain each vertice as a key and the list of adjacent vertices of that vertices as a value.

For our example above, the adjacency list representation will look as follows:

We can see that the adjacency list is much less expensive on memory as the adjacency matrix is very sparse.

Most graph algorithms involve visiting each vertex in \(V\), starting from a root node \(v_0\). There are several ways of achieving this. The two most common traversal algorithms are breadth-first search and depth-first search.

In a breadth-first search , we start with the start node, followed by its adjacent nodes, then all nodes that can be reached by a path from the start node containing two edges, three edges, and so on. Formally the BFS algorithm visits all vertices in a graph \(G\), that are \(k\) edges away from the source vertex \(s\) before visiting any vertex \(k+1\) edges away. This is done until no more vertices are reachable from \(s\). The image below demonstrates exactly how this traversal proceeds:

For a graph \(G = (V,E)\) and a source vertex \(v\), breadth-first search traverses the edges of \(G\) to find all reachable vertices from \(v\). It also computes the shortest distance to any reachable vertex. Any path between two points in a breadth-first search tree corresponds to the shortest path from the root \(v\) to any other node \(s\).

We may think of three types of vertices in BFS as tree verties, those that have been taken of the data structure. fringe vertices, those adjacent to tree vertices but not yet visited, and undiscovered vertices, those that we have not encountered yet. If each visited vertex is connected to the edge that caused it to be added to the data structure, then these edges form a tree.

To search a connected component of a graph systematically, we begin with one vertex on the fringe, all others unseen, and perform the following step until all vertices have been visited: "move one vertex \(x\) from the fringe to the tree, and put any unseen vertices adjacent to \(x\) on the fringe." Graph traversal methods differ in how it is decided which vertex should be moved from the fringe to the tree. For breadth-first search we want to choose the vertex from the fringe that was least recently encountered; this corresponds to using a queue to hold vertices on the fringe.

What is the state of the queue at each iteration of BFS, if it is called from node 'a'? PP The table below shows the contents of the queue as the procedure. BFS visits vertices in the graph above. BFS will visit the same vertices as DFS. In this example all of them. \[\begin{array}{l|r} \textbf{Node Visited} & \textbf{Queue} \\ \hline \text{a} & \text{a} \\ \text{ } & \text{(empty)} \\ \text{b } & \text{b} \\ \text{f } & \text{b f} \\ \text{i} & \text{b f i} \\ \text{ } & \text{f i} \\ \text{c} & \text{f i c} \\ \text{e} & \text{f i c e} \\ \text{ } & \text{ i c e} \\ \text{g } & \text{ i c e g} \\ \text{ } & \text{ c e g} \\ \text{ } & \text{ e g} \\ \text{d } & \text{ e g d} \\ \text{ } & \text{ g d} \\ \text{ } & \text{ d} \\ \text{ } & \text{ (empty)} \\ \text{ h} & \text{ h} \\ \text{ } & \text{ (empty) } \end{array}\]

Depth-first search explores edges out of the most recently discovered vertex \(s\)  that still has unexplored edges leaving it. Once all of ’s edges have been explored, the search “backtracks” to explore edges leaving the vertex from which  was discovered. This process continues until we have discovered all the vertices that are reachable from the original source vertex. If any undiscovered vertices remain, then depth-first search selects one of them as a new source, and it repeats the search from that source. The algorithm repeats this entire process until it has discovered every vertex:

• Visit a vertex \(s\).
• Mark \(s\) as visited.
• Recursively visit each unvisited vertex attached to \(s\).

A recursive implementation of DFS:

A non-recursive implementation of DFS, it delays whether a vertex has been discovered until the vertex has been popped from the stack.

Similar to tree traversal, the code for breadth-first search is slightly different from depth-first search. The most commonly mentioned difference is that BFS uses a queue to store alternative choices instead of a stack. This small change however leads to a classical graph traversal algorithm. Depth-first search goes down a single path until the path leads to the goal or we reach a limit. When a path is completely explored we back track. BFS however explores all paths from the starting location at the same time.

As we increase the size of our graph, the contrast between depth-first and breadth-first search is quite evident. Depth-first search explores the graph by looking for new vertices far away from the start point, taking closer vertices only when dead ends are encountered; breadth-first search completely covers the area close to the starting point, moving farther away only when everything close has been looked at. Again, the order in which the nodes are visited depends largely upon the effects of this ordering on the order in which vertices appear on the adjacency lists.

John lives in the Trees of Ten Houses, and it is a most ideal and idyllic place for him and the other dwellers up in the canopy. They have invested a tremendous amount of time in engineering these houses, and to ensure no house felt isolated from the others, they built a fresh, finely crafted bridge between each and every house!

Unfortunately, the Trees of Ten Houses were not immune to thunderstorms, nor were the bridges well engineered. The night was treacherous, howling with wind and freezing with rain, so the odds for the bridges were not good--each bridge seemed just as likely to survive as to be shattered!

Fortunately, as there were so very many bridges in the Trees of Ten Houses, when John did wake the following morning, he found he was able to make his way to each and every house using only the existing bridges, though round-about routes may have been necessary. As they began rebuilding, John became curious... what were the chances that they'd all be so lucky?

More formally, if \(P\) is the probability that, after the storm, John is able to traverse to each and every house, what is \(\big\lfloor 10^{10} P \big\rfloor?\)

• The Trees of Ten Houses do, in fact, contain precisely 10 houses.
• Before the storm, there exists a single bridge between each and every unique pair of houses.
• The storm destroys each bridge with independent probability \(\frac{1}{2}\).
• John is allowed to traverse through others' houses to try to reach all of them, but he must only use the surviving bridges to get there. No vine swinging allowed.

Tagged under #ComputerScience as this problem is quite tedious to do without it, though not impossible.

Image credit: http://hdscreen.me/wallpaper/2645876-bridges-fantasy-art-landscapes-mountains.

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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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• Graphical Representation

What is a Graph

In mathematics, a graph is a diagrammatic illustration that is used to represent data values in a systematic, organized and understandable manner.  It is indeed a very tedious task to analyze lots of data. However, when the same numerical data is represented in a pictorial form, it becomes easy to understand the relationship between the provided data objects and the concepts represented. It is often said that a picture is worth a thousand words. Therefore, graphs are particularly useful when it comes to displaying and analyzing data. 

The data have shown on the graph usually represents a relationship between various things for comparison among them. It could also help us to understand the changing trends over some time. With the help of graphs, it becomes easier to comprehend information.

Types of Graphical Representation 

To represent various kinds of data, different kinds of graphs are used. Some of the commonly used graphs are as follows: 

In a line graph, a line shows trends in data. It can also be used to predict the changing trends of the displayed data objects in the future. 

A bar graph is used when data has been categorized or sorted. It is the best kind of graph for comparing data. In this, solid bars are used to represent different categories or data values.

A histogram is similar to a bar graph. However, instead of making comparisons, it groups the numerical data into ranges. It is most commonly used to show frequency distributions. 

Pie or Circle Graph

In a pie chart, a circle represents statistical graphics. It is divided into many slices or pies to represent the proportion of numbers. The length of the arc of each pipe corresponds to the quantity represented by it.

Stem and Leaf Graph

A stem and leaf plot is a special type of table in which the data values are divided into a stem, which represents the initial digit or digits, and a leaf, which usually represents the last digit. 

How to plot the Data Accurately on Graphs?

It is of utmost importance that the information which is being represented graphically should be accurate and easy to understand. The various points that should be kept in mind are: 

The scale chosen to plot the graph should be according to the data values that have to be represented.

The index makes it easier for the reader to read and interpret the data represented by various colours, patterns, designs, etc.

The Source of Data

As and when necessary, the source of data can be mentioned at the bottom of the graph. 

The purpose of making the graph is defeated if the representation does not look tidy. Hence, it must be ensured that the data so represented is neat and visually appealing. 

There is no need to unnecessarily complicate the graph. The simpler, the better.

Basics of Graphical Representation

A graph usually consists of two lines called the coordinate axes. The horizontal line is called the x-axis, and the vertical line is called the y axis. The intersection of the two axes is the point of origin. The values on the x-axis towards the right of the origin are considered positive, and towards the left are negative. Similarly, on the y-axis, the values above the origin will be positive and the values below the origin will be negative. 

 Benefits of using Graphs 

Graphs save time. If the same information is written down, it becomes a period process to spot the trends and be able to analyze the data properly. 

A graph can be used to represent information neatly and also takes less space.

It is easy to understand.

Analysing a graphical representation of data does not take much and helps in making quick decisions. 

Graphs give you a summarized version of a long report that contains a large amount of data. 

Graphs and tables are less likely to have any errors and mistakes. 

Graphical representation of two or more data sets will allow you to compare the information and take preventive measures to avoid mistakes in the future. 

By making the data easy to understand, graphs eliminate the literacy barriers so that anyone can analyse and interpret the presented data. 

With just a glance at the graphical representation, a person can make quick and informed decisions.  

Some Rules for Graphical Representation of Data 

Like any other mathematical concept, graphical representation also has some rules you must follow. These rules will help you present the information on a graph effectively. Below are the rules for graphical representation of data: 

When you are making a graph, you should give it an appropriate title that highlights the subject of the given data.

While making a graph, do not forget to mention the measurement unit. 

Make an index using colours, designs, shades, lines, etc. to make the graphical representation easier to understand.  

You have to choose an appropriate scale to represent the given set of data. 

Construct the graph as simple as possible so that everyone can easily understand the presented data.

Whether you are making a pie chart or a bar graph, it should look neat and clean so that the teacher can easily read the figures. 

Importance of Graphical Representation 

Graphical representation gives you a visual presentation of the given data to make it easier to understand. Graphs help you identify different patterns over a short and long period. It assists you in the interpretation of data and comparison of two or more data sets. Here are reasons why graphical representation is important: 

Graphs are widely accepted in the corporate world as it summarises the data into an understandable format and avoids wastage of time. 

When you want to compare two or more different data sets, graphs are your best choice. A graphical representation of all the data sets will allow you to quickly analyze the information and help you in making quick decisions. 

Through descriptive reports and information, it becomes difficult to make decisions. However, with graphs, the management can analyse the situation more clearly and make the right decisions. 

With tables and graphs, the information can be presented in an organised and logical manner, making it easier to understand for anyone. 

Graphical representation of data does not demand much of your time, improving the overall efficiency. You can quickly make the graphs within minutes and focus on other important work. 

Qualitative representation might include many grammatical errors and other mistakes that can mislead the person reading it. Since graphs involve numerical representation of data, there are fewer chances of errors and mistakes. 

Graphs give you the entire summary of a large amount of data.    

FAQs on Graphical Representation

1. What is a frequency polygon graph?

A frequency polygon graph can be used to represent the same set of data which is represented by a histogram. In this type of graph, lines are used to connect the midpoints of each interval. The frequencies of the data interval are represented by the height at which the midpoints are plotted in the graph. A frequency polygon can be created using the already drawn histogram, or by calculating the midpoint from the intervals of the frequency distribution table. To calculate the midpoint, we need to find the average of the upper and the lower values of the interval/range. 

Frequency polygon gives us an idea regarding the shape of the data and the trends that it follows during a particular duration of time. 

Steps to draw a frequency polygon: 

Calculate the classmark for each interval, which is equal to (upper limit + lower limit)/2. 

Represent the class marks on the x-axis and their corresponding frequencies on the y-axis. 

For every class mark on the x-axis, plot the frequencies of the y-axis.  

Join all the obtained points to get a curve.

The figure obtained is called a frequency polygon. 

2. What is the difference between a Bar Graph and a Histogram?

The most commonly visible difference between a bar graph and a histogram is that, in a bar graph, the bars have spaces between them, whereas, in a histogram, the bars are drawn adjacent to each other, without leaving any spaces. 

As they both make use of bars to represent the data, it becomes slightly difficult to understand the fundamental difference between the two. A histogram is a graphical representation that uses bars to demonstrate the frequency of numerical data. In a histogram, elements are grouped, so they can be considered as ranges.

A bar graph is a diagrammatic representation that uses bars for the comparison of different categories of data.  The plotted elements are treated as individual entities, and not as a range. The bars can be drawn horizontally or vertically. The height of the bar corresponds to the size of the data object.

3. From which platform can I learn Graphical Representation?

Vedantu is the best e-learning platform from where you can learn Graphical Representation. To start studying the concept of graphical representations, you can visit our official website or download our mobile app from the app store or play store. Our learning platform is available to all students across the globe for absolutely free. Apart from the Graphical Representation, you will find plenty of study material for different topics of Maths. From the website, you can learn concepts, such as Number System, Area of Triangle, Factorisation, and much more.    

4. What are the advantages of a Bar Graph?

A bar graph is the most widely used method of graphical representation. Below are some of the advantages of a bar graph: 

A bar graph shows every category from the given frequency distribution. 

Bar graphs summarize a large chunk of data into a simple, understandable, and interpretable form. 

With a bar graph, you can easily compare two or more different data sets. 

You can study the varying patterns in a bar graph over a long period. 

A bar graph makes the trends easier to highlight than other types of graphical representation.  

5. How to decide which graph is suitable for a situation?

Sometimes, the question does not specify which type of graph you have to use. In these cases, you will have to analyze the given data and decide which graph will be more suitable. When you have to compare two different categories of data sets, you should use a bar graph as it makes the data easy to interpret. If you have to find the trends and progress over a short period, you can use line graphs. Moreover, when you have to represent a whole graphically, a pie chart is the best option.   

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WikiGraphs is collected by pairing each Wikipedia article from the established WikiText-103 benchmark with a subgraph from the Freebase knowledge graph. This makes it easy to benchmark against other state-of-the-art text generative models that are capable of generating long paragraphs of coherent text. Both the graphs and the text data are of significantly larger scale compared to prior graph-text paired datasets.

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