define graphical representation in math

Graph – Definition, Types, FAQs, Practice Problems, Examples

What is a graph .

• Types of Graphs

Solved Examples On Graph

Practice problems on graph, frequently asked questions on graph.

In math, a graph can be defined as a pictorial representation or a diagram that represents  data  or values in an organized manner.   The points on the graph often represent the relationship between two or more things. 

Here, for instance, we can represent the data given below, the type and number of school supplies used by students in a class, on a graph. We begin by counting each supply and representing the data in particular colors in a systematic order in a table. 

We can also represent the data using a bar graph. The number of each of the supplies is represented with bars. The height of the bar, the more is the number of the supply or items used.

Types of Graphs:

The representation of the information through pictures is called pictograph . A certain number of items is represented by each picture. For example, you can use a picture of a cricket bat to display how many cricket bats are sold by a shop during a certain week.

In this pictograph, 1 picture of the cricket bat represents 4 cricket bats. So, according to the graph, 12 bats (4 + 4 + 4) were sold on Tuesday.

A bar graph is the representation of numerical data by rectangles (or bars) of equal width and varying height. The gap between one bar and another is uniform throughout. Bar graphs can be either horizontal or vertical. The height or length of each bar relates directly to its value.

Line Graph:

A line graph uses dots connected by lines to show the changes over a period of time.

The pie chart is also known as a circle graph. It shows how a whole is divided into different parts. The pie chart shows the relative size of each data set in proportion to the entire data set. Percentages are used to show how much of the whole each category occupies.

Related Worksheets

Example1: State whether the given statements are true or false.

• In a bar graph, the width of bars may not be equal.
• In a bar graph, bars of uniform width can be drawn both vertically as well as horizontally.
• In the bar graph, the gap between two consecutive bars may not be the same.
• In the bar graph, each bar represents only one value of numerical data.
• False. In a bar graph, bars have equal width.
• False. In a bar graph, the gap between two consecutive bars should be the same.

Example 2: Name the type of each of the given graphs.

______________________________

(a) Bar graph

(b) Pie chart

(c) Pictograph

(d) Line graph

Example 3: Refer to the given pictograph and answer the questions.

• Which was the most popular flavor?
• 60 cones of which flavor was sold?
• How many vanilla flor cones were sold?
• How many total cones were sold?
• Mint Chocolate Chip

Example 4: Read the bar graph and answer the questions.

(a) How many push-ups were done on Thursday?

(b) On which day no push-ups were done?

(c) On which day maximum push-ups were done?

(d) Sam’s target was to do at least 140 push-ups in the week. Check if Sam was able to achieve his target not.

(b) Wednesday

(d) Total pushups done in a week = 15 + 20 + 0 + 25 + 20 + 30 + 35 = 145 push ups So, 5 more pushups should have been done to complete the target of 150.

Attend this Quiz & Test your knowledge.

A circular graph in which each sector represents a particular quantity is called a:

Which type of graph displays data that changes continuously over a period of time, which type of graph represents data with rectangles of uniform width, a pictograph uses the following two images. use the information below to find the unknown value:.

What is data?

Data is a collection of facts gathered to give some meaningful information.

What differentiates data from information?

Data is a collection of numerical facts in raw and unorganized form. Information is the processed data arranged in an organized and structured form.

Why do we need to learn data representation?

Representing data in visual form or graphs gives a clear idea of what the information means and makes it easy to comprehend and identify trends and patterns.

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Graphs of Statistical Data

Exponential graphs, graphs on a logarithmic scale, graph showing the distribution of frequencies, frequency polygon graph, cumulative frequency graph, graph|definition & meaning.

In mathematics, a graph is a graphical representation (also known as a diagram) that conveys information (such as data or values) in an orderly way. Most of the time, the dots on the graph demonstrate the connection between two or more different things.

Type of Graphs 

The following is a list of the sorts of graphs that are most frequently used: Graphs of statistical data (bar graph, pie graph, line graph, etc.), exponential graphs, graphs on a logarithmic scale, trigonometric graphs, graphs showing the distribution of frequencies, etc.

Each of these graphs is utilized in various contexts to condense the representation of a particular set of facts. The specifics of these graphs (or charts) are broken down in the following paragraphs.

Bar, line, pie, and histogram charts are the four fundamental graphs utilized in statistical analysis. These are discussed in greater detail below.

A bar graph is a pictorial depiction of grouped data that displays the data in the form of vertical or horizontal bars of varying lengths, with each bar’s length proportional to the data’s value. The categorical data is represented by the chart’s horizontal axis , while the chart’s vertical axis defines the discrete data.

Figure 1: Representation of data by bar graph

As you can see from the above figure, a statistical graph or chart is a pictorial depiction of statistical data in the form of a graphical chart. It is much simpler to comprehend and make sense of statistical information when it is represented through statistical graphs depicting data sets.

It is a type of graph that illustrates change over a while via the use of points and lines. In other words, it is a chart that illustrates a line connecting numerous points or a line that illustrates the link between them . The graphic illustrates quantitative information between two variables associated by connecting a sequence of succeeding data points with either a straight path or a curve. The line or curve may be straight or curved. A linear chart’s vertical and horizontal axes are used to compare and contrast these two variables.

A histogram is a chart that uses connected rectangular bars to illustrate the frequency of continuous and discrete data within a dataset. In this case, the number of measurements shown to fall within a predetermined class interval is depicted by a bar chart in the shape of a rectangle.

A numerical representation of a dataset that uses a pie chart to show the proportions of the data . To draw this graph, a circle is segmented into several sectors, and the proportion of one element that makes up the whole of each sector is represented by the circle as a whole. A circle graph or circle chart is another name for this type of chart.

Figure 2: Representation of data by pie chart

The depiction of exponential functions that use a table of values and drawing the points on lined paper is called an exponential graph. It should be noted that the logarithmic functions are the opposite of the exponential functions. When it comes to exponential graphs, the graph might take the form of either an ascending or a descending curve , depending on the function. An illustration of how to graph an exponential function is provided below for your convenience, and it will make the topic much simpler to grasp.

The reverse of exponential functions are logarithmic functions, and the methods for charting logarithmic and exponential functions are comparable. To draw logarithmic graphs, a table of values must be created, and then the points must be plotted on graph paper in accordance with the table. The inversion of an exponential curve will always be represented graphically by a log function.

Figure 3: Representation of logarithmic graph

It is possible to demonstrate the frequency of the events in a particular sample by employing a frequency distribution graph . The table of values produced for frequency distribution graphs by arranging the outcomes in one column and the number of instances that occur (i.e. frequency) in another column.

A histogram is used to analyze different data sets or depict a cumulative frequency distribution , and a frequency polygon is virtually indistinguishable from one another. It employs a line graph to display quantitative data. The field of statistics is concerned with systematically gathering information and data for analytical purposes. In cricket, the game’s statistic is determined by tallying up the number of runs scored for each ball. Many tables, graphs, pie charts, bar graphs, histograms, and polygons display statistical data graphically. Frequency polygons are highly recommended as a visually powerful technique for displaying quantifiable information and its frequencies.

In the field of statistics, the term “cumulative frequency” refers to the sum of individual frequencies that are broken down into various class intervals. It signifies that the information and the total are given in the form of a table, and within that table, the frequencies are spread in accordance with the class interval.

Examples of Graphs

How to find distance on a coordinate plane between two points?

Let the two numbers in a plane be R (1, 2) and S (0, 3).

The distance between the points R and S can be computed with the distance formula, which is:

\[ \mathsf{\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}} \]

Here, x 1 = 1, x 2 = 0, y 1 = 2 and y 2 = 3.

After putting values in it, we get:

$\mathsf{\sqrt{(0-1)^2+(3-2)^2}}$ = 2

$\mathsf{\sqrt{2}}$ = 1.414

How to find distance between coordinates in 3 dimensional space?

In 3-dimensional space we also have z-axis, so the formula becomes:

\[\mathsf{\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}}\]

If the coordinates are:

x 1 = 2, x 2 = 4, y 1 = 1, y 2 = 3, z 1 = 4 and z 2 = 5

then after using the above formula the answer we get is 3.

All images/graphs are created using GeoGebra.

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• Graphs and Graphical Representation

What are Graphs and Graphical Representation?

Graphical representation refers to the use of charts and graphs to visually analyze and display, interpret numerical value, clarify the qualitative structures. The data is represented by a variety of symbols such as line charts, bars, circles, ratios. Through this, greater insight is stuck in the mind while analyzing the information. 

Graphs can easily illustrate the behavior, highlight changes, and can study data points that may sometimes be overlooked. The type of data presentation depends upon the type of data being used. 

Graphical Representation of Data

The graphical representation is simply a way of analyzing numerical data. It comprises a relation between data, information, and ideas in a diagram. Anything portrayed in a graphical manner is easy to understand and is also termed as the most important learning technique. The graphical presentation is always dependent on the type of information conveyed. There are different types of graphical representation. These are as follows:

Line Graphs: 

Also denoted as linear graphs are used to examine continuous data and are also useful in predicting future events in time.

Histograms: 

This graph uses bars to represent the information. The bars represent the frequency of numerical data. All intervals are equal and hence, the width of each bar is also equal.

Bar Graphs: 

These are used to display the categories and compare the data using solid bars. These bars represent the quantities.

Frequency Table: 

This table shows the frequency of data that falls within that given time interval. 

Line Plot: 

It shows the frequency of data on a given line number.

Circle Graph: 

It is also known as a pie chart and shows the relationship between the parts of the whole. The circle consists of 100% and other parts shown are in different proportions.

Scatter Plot: 

The diagram shows the relationship between two sets of data. Each dot represents individual information of the data.

Venn Diagram: 

It consists of overlapping circles, each depicting a set. The inner-circle made is a graphical representation.

Stem and Leaf Plot: 

The data is organized from the least value to the highest value. The digits of the least place value form the leaf and that of the highest place value form the stem.

 Box and Whisker Plot: 

The data is summarised by dividing it into four parts. Box and whisker show the spread and median of the data.

Graphical Presentation of Data - Definition

It is a way of analyzing numerical data. It is a sort of chart which shows statistical data in the form of lines or curves which are plotted on the surface. It enables studying the cause and effect relationships between two variables . It helps to measure the extent of change in one variable when another variable changes. 

Principles of Graphical Representation

The variables in the graph are represented using two lines called coordinate axes. The horizontal and vertical axes are denoted by x and y respectively. Their point of intersection is called an origin ‘O’. Considering x-axes, the distance from the origin to the right will take a positive value, and the distance from the origin to the left will take a negative value. Taking the same procedure on y-axes. The points above origin will take the positive values and the points below origin will take negative values. As discussed in the earlier section about the types of graphical representation. There are four most widely used graphs namely histogram, pie diagram, frequency polygon, and ogive frequency graph.

Rules for Graphical Representation of Data

There are certain rules to effectively represent the information in graphical form. Certain rules are discussed below:

Title: One has to make sure that a suitable title is given to the graph which indicates the presentation subject.

Scale: It should be used efficiently to represent data in an accurate manner.

Measurement unit: It is used to calculate the distance between the box

Index: Differentiate appropriate colors, shades, and design I graph for a better understanding of the information conveyed.

Data sources: Include the source of information at the bottom graph wherever necessary. It adds to the authenticity of the information. 

Keep it simple: Construct the graph in an easy to understand manner and keep it simple for the reader to understand. Looking at the graph the information portrayed is easily understandable. 

Importance of Graphical Representation of Data

Some of the importance and advantages of using graphs to interpret data are listed below:

The graph is easiest to understand as the information portrayed is in facts and figures. Any information depicted in facts, figures, comparison grabs our attention, due to which they are memorizable for the long term.

It allows us to relate and compare data for different time periods.

It is used in statistics to determine the mean , mode, and median of different data.

It saves a lot of time as it covers most of the information in facts and figures. This in turn compacts the information.

FAQs on Graphs and Graphical Representation

Q1. State the Advantages and Disadvantages of Graphical Representation of Data?

Ans: These graphical presentations of data are vital components in analyzing the information. Data visualization is one of the most fundamental approaches to data representation. Its advantages include the following points:

Facilitates and improves learning

Flexibility of use

Understands content

Increase structure thinking

Supports creative thinking

Portrays the whole picture

Improves communication

With advantages, certain disadvantages are also linked to the graphical representation. The disadvantages concern the high cost of human effort, the process of selecting the most appropriate graphical and tabular presentation, creative thinking, greater design to interpret information, visualizing data, and as human resource is used. The potential for human bias plays a huge role.

Q2. What is the Graphical Representation of Data in Statistics?

Graphs are powerful data evaluation tools. They provide a quick visual summary of the information. In statistics information depicted is of mean, mode, and median. Box plots, histograms are used to depict the information. These graphs provide information about ranges, shapes, concentration, extreme values, etc. It studies information between different sets and trends whether increasing or decreasing. Since graphical methods are qualitative, they are not only the basis of comparison and information.

Data Handling

Data handling is considered one of the most important topics in statistics as it deals with collecting sets of data, maintaining security, and the preservation of the research data. The data here is a set of numbers that help in analyzing that particular set or sets of data. Data handling can be represented visually in the form of graphs. Let us learn more about this interesting concept, the different graphs used, and solve a few examples for better understanding.

Definition of Data Handling

Data Handling is the process of gathering, recording, and presenting information in a way that is helpful to analyze, make predictions and choices. Anything that can be grouped based on certain comparable parameters can be thought of as data . Parameters mean the context in which the comparison is made between the objects. Data handling usually represent in the form of pictographs, bar graphs, pie charts, histograms , line graphs, stem and leaf plots , etc. All of them have a different purpose to serve. Have a look at the composition of the air that we have learned about in our science classes.

The constituents of air are presented with different colors in the form of parts of a pie. Do you think, a bar chart, line graph, or any other graphical representation would be able to communicate the information as effectively as this one. Definitely no. With a detailed study of each of them, you can clearly understand the purpose of each of them and use them suitably.

Types of Data

Data handling is performed depending on the types of data. Data is classified into two types, such as Quantitative Data and Qualitative Data. Quantitive data gives numerical information, while qualitative data gives descriptive information about anything. Quantitative can be either discrete or continuous data.

Important Terms in Data Handling

In data handling, there are 4 important terms or most frequently used terms that make it simple to understand the concept better. The terms are:

• Data: It is the collection of numerical figures of any kind of information
• Raw Data: The observation gathered initially is called the raw data.
• Range: It is the difference between the highest and lowest values in the data collection.
• Statistics : It deals with the collection, representation, analysis, and interpretation of numerical data.

Steps Involved in Data Handling

Following are the steps to follow in data handling:

Graphical Representation of Data Handling

Data handling can be represented in a number of graphical ways. Here is a list of various types of graphical representations of data that are very effective in data handling.

Bar graphs represent data in the form of vertical or horizontal bars showing data with rectangular bars and the heights of bars are proportional to the values that they represent. Bar graphs help in the comparison of data and this type of graph is most widely used in statistics. Look at the image below as an example.

Pictographs or Picture Graphs

Pictograph is a type of graph where information is represented in the form of pictures, icons, or symbols. It is the simplest form of representing data in statistics and data handling. Since the use of images and symbols are more in a pictograph, interpreting data is made easy along with representing a large number of data. Look at the example below for a better understanding.

Line Graphs

In data handling the data represented in the form of a line on a graph is the line graph . The graph helps in showcasing the different trends or changes in the data. The line segment plotted on the graph is constructed by connecting individual data points together. Look at the example below to understand it better.

A pie chart is data represented in a circular graph divided into smaller sectors to denote certain information. Pie charts help in showcasing the profit and loss for a business, while in school in showcasing the number depending on the data. This kind of chart is widely used in marketing sales. Look at the example below, the pie chart shows how people like the mentioned fruits from a group of 360.

Scatter Plot

Scatter plot represents the points and then the best fit line is drawn through some of the points. Any 3D data in data handling can be represented by a scatter plot. Look at the example below to understand it better.

Related Topic

Listed below are a few interesting topics related to data handling. Take a look.

• Absolute Value Graph
• Frequency Distribution Table
• Probability and Statistics

Examples on Data Handling

Example 1: Henry wants to introduce his 5-year-old daughter to data handling. Which type of graphical representation can he use for this?

As his daughter is just 5 years old, he should prefer using Pictograph to introduce data handling. In this representation, simple pictures like circles, stars are drawn to represent different data.

Example 2: How is data represented graphically?

Solution: Various types of graphs that can be used for representing data are:

• Scatter plot
• Pie chart/ Circle chart
• Picture graph

Depending on the purpose, a suitable graph can be chosen.

Example 3: Here is a review of an electronic product. Out of all the people who gave their reviews, 16 of them gave a 5-star rating to the product. Can you find out how many people provided their feedback in all?

Let the total reviews be x.

Number of people who gave 5 star = 16

Percentage of people who gave 5 star = 64%

So, number of people who gave 5 star = 64 % × x

16 = 64/100 × x

x = (16 × 64)/100

Therefore, 25 people gave reviews for the product

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Practice Questions on Data Handling

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FAQs on Data Handling

What is data handling.

Data Handling is the process of gathering, recording, and presenting information in a way that is helpful to analyze, make predictions and choices. There are two types of data handling namely quantitative data and qualitative data. Data handling can be represented through various graphs.

What are the Two Types of Data Handling?

The two types of data handling are qualitative data and quantitative data. Quantitive data gives numerical information, while qualitative data gives descriptive information about anything. Quantitative can be either discrete or continuous data.

What are the Steps Involved in Data Handling?

The six steps that are involved in data handling are:

• Collection of Data
• Presentation of Data
• Graphical Representation of Data
• Analyzing the Data

What are the Types of Graphical Representations in Data Handling?

There are numerous types of graphical representation for the data that are available. Some of the most extensively used graphical representations are :

What is the Difference Between Data and Information in Data Handling?

The term data refers to the collection of certain facts that are quantitive in nature like height, number of children, etc. Information on the other hand is a form of data after being processed, arranged, and presented in a form that gives meaning to the data.

What is the Difference Between the Chart and Graph?

The difference between chart and graph can be understood from the fact that - All graphs are charts but every chart is not a graph. Charts display data in the form of a diagram, table, or graph. So, the graph is just a pictorial way of presentation of information.

Mathematical Representations

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• First Online: 01 January 2020
• Cite this reference work entry

• Gerald A. Goldin 2  

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Definitions

As most commonly interpreted in education, mathematical representations are visible or tangible productions – such as diagrams, number lines, graphs, arrangements of concrete objects or manipulatives, physical models, written words, mathematical expressions, formulas and equations, or depictions on the screen of a computer or calculator – that encode, stand for, or embody mathematical ideas or relationships. Such a production is sometimes called an inscription when the intent is to focus on a specific instance without referring, even tacitly, to any interpretation of it. To call something a representation thus includes reference to some meaning or signification it is taken to have. Such representations are called external – i.e., they are external to the individual who produced them and accessible to others for observation, discussion, interpretation, and/or manipulation. Spoken language, interjections, gestures, facial expressions, movements, and postures may sometimes...

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Goldin, G.A. (2020). Mathematical Representations. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_103

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• Trigonometry

Representation of a Set

• Math Doubts

A method of expressing a collection of well-defined objects is called the representation of a set .

Introduction

There is a purpose for introducing the concept of a set in mathematics. Hence, it is essential to express it in a special way in mathematics.

There are two different ways to express a set in mathematics.

Graphical representation

Mathematical representation.

Now, let’s understand the basic representation of a set from understandable examples.

In general, the objects are collected in closed packets. The same principle can also be used in set theory to represent the collection of well-defined objects. Therefore, a set can be represented graphically by a closed geometric shape.

There are several closed geometric shapes in geometry. Hence, a set can be represented by any one of the closed geometric shapes.

For example, a circle, a triangle, a square, or any other closed geometric shape.

There are two common problems in expressing the sets in graphical representation.

• Expressing the different sets in either a closed geometric shape or different closed geometric shapes confuse us, and it irritates us.
• It is not actually convenient for us to express a set more than once in the form of graphical representation in mathematics.

For overcoming the above two issues, the mathematical representation was introduced in set theory. In this method, we represent every set by a name and they are usually denoted by uppercase (or capital) letters.

For example, we have three sets and they are denoted by capital letters $A$, $B$ and $C$. They are called Set $A$, Set $B$ and Set $C$.

Advanced example

A set of first five natural numbers.

$1, 2, 3, 4,$ and $5$ are first five natural numbers. Display the first five natural numbers inside any closed geometrical shape for representing this set graphically.

Similarly, write the first five natural numbers with comma separation inside the curly braces.

$\Big\{\, 1, 2, 3, 4, 5 \,\Big\}$

Representation

List of the mathematical methods to learn how to express a set in different mathematical approaches.

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• Quadratic Equations
• Hyperbolic functions
• Straight Lines
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Teaching with Jillian Starr

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FREE Number Talks

First grade teachers, access 20 FREE Number Talk Prompts to enhance your place value unit and get your students engaged in conversation.

Mathematical Representations Series Part 4: Verbal Representation

Welcome back to our deep dive into mathematical representations! Today, we are taking a look at symbolic representations and how we can translate between symbolic, concrete, and visual representations. First, let’s do a two-sentence recap of this series so far:

We have already focused on concrete representations and the immense value of manipulatives, the range of visual representations we want to encourage with our students, and how we can use numerals and operations to represent thinking symbolically . We are centering our conversation around Lesh’s Translation Model, which encompasses the range of ways we represent our thinking, and stresses the importance of making connections between representations.

Today we are talking about verbal representations. While it’s an essential form of representation for our students, it is often less discussed. This is likely due to the fact that it is not explicitly called out in the Concrete-Pictorial Abstract model . This is just another reason why I love introducing teachers to Lesh’s translation model alongside the CPA (often called CRA) model.

Verbal Representation

The language we use to communicate our thoughts and ideas is another equally important representation. This can be oral, written, signed, or any way that a student would look to communicate language. James Heddens writes that students “need to be given opportunities to verbalize their thought processes: verbal interaction with peers will help learners clarify their own thinking.”

If we go back to our previous examples from concrete, visual, and abstract thinking, we have a student with five yellow counters and four red counters. The student then sketched their counters and wrote the number sentence 5+4=9 on their paper.

So how does verbal representation come into play? Perhaps after the activity, a student shows you their sketch of the counters. When you ask them about their drawing, they may share “I had nine counters. Four of them were red and five of them were yellow, and that makes nine.” That statement is a verbal representation of the concept. They have also just translated their visual representation to a verbal representation.

Connecting Two Verbal Representations

If wanted, we could take it a step further by asking the student to write their thoughts down. This will require the student to revisit their thoughts communicated orally and condense them into a written description, like “Four counters and five counters make nine counters.” This extra step of condensing their language into a second form, allowed students to connect two verbal representations. WOW!

Verbal representation is essential to our work, especially in the early grades. Our students who may not have the ability to write words or numbers will often communicate their understanding orally. This NEEDS to be a part of the discussion when we talk about deepening student understanding, and it’s a huge reason why I make sure to consider Lesh’s Translation Model in addition to the Concrete-Pictorial-Abstract model.

What’s Up Next?

This series is going to dive deep into each of the representations discussed in Lesh’s Translation Model, and then we are going to put it all together so we can make a big impact on your math teaching this year.

If you missed Part One about Concrete Representations , Part Two about Visual Representations , or Part Three about Symbolic Representations , check them out so you have all of the info you need before we move on!

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• Math Article
• Types Of Graphs

Types of Graphs in Statistics

There are different types of graphs in mathematics and statistics which are used to represent data in a pictorial form. Among the various types of charts or graphs , the most common and widely used ones are explained below.

Table of Contents:

Types of Graphs and Charts

• Statistical graphs
• Exponential graphs
• Logarithmic graphs
• Trigonometric graphs
• Frequency distribution graph

The list of most commonly used graph types are as follows:

• Statistical Graphs (bar graph, pie graph, line graph, etc.)

Exponential Graphs

Logarithmic graphs, trigonometric graphs, frequency distribution graph.

All these graphs are used in various places to represent a specific set of data concisely. The details of each of these graphs (or charts) are explained below in detail which will not only help to know about these graphs better but will also help to choose the right kind of graph for a particular data set.

Statistical Graphs

A statistical graph or chart is defined as the pictorial representation of statistical data in graphical form. The statistical graphs are used to represent a set of data to make it easier to understand and interpret statistical information. The different types of graphs that are commonly used in statistics are given below.

The four basic graphs used in statistics include bar, line, histogram and pie charts. These are explained here in brief.

Bar graphs are the pictorial representation of grouped data in vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data. The chart’s horizontal axis represents categorical data, whereas the chart’s vertical axis defines discrete data.

Click here to know more about bar graphs and its types.

A graph that utilizes points and lines to represent change over time is defined as a line graph . In other words, it is a chart that shows a line joining several points or a line that shows the relation between the points. The diagram depicts quantitative data between two changing variables with a straight line or curve that joins a series of successive data points. Linear charts compare these two variables on a vertical and horizontal axis.

A histogram chart displays the frequency of discrete and continuous data in a dataset using connected rectangular bars. Here, the number of observations that fall into a predefined class interval represented by a rectangular bar.

Learn more about histogram and its type here.

A pie chart used to represent the numerical proportions of a dataset. This graph involves dividing a circle into various sectors, where each sector represents the proportion of a particular element as a whole. This is also called a circle chart or circle graph.

Exponential graphs are the representation of exponential functions using the table of values and plotting the points on a graph paper. It should be noted that the exponential functions are the inverse of logarithmic functions. In the case of exponential charts, the graph can be an increasing or decreasing type of curve based on the function. An example is given below, which will help to understand the concept of graphing exponential function easily.

For example, the graph of y = 3 x is an increasing one while the graph of y = 3 -x is a decreasing one.

Graph of y = 3 x :

Logarithmic functions are inverse of exponential functions and the methods of plotting them are similar. To plot logarithmic graphs , it is required to make a table of values and then plot the points accordingly on a graph paper. The graph of any log function will be the inverse of an exponential function. An example is given below for better understanding.

For example, the inverse graph of y = 3 x will be y = log 3 {x} which will be as follows:

Trigonometry graphs are plotted below for the 6 trigonometric functions, which include sine function, cosine function, tangent function, cotangent function, cosec function, and sec function. Visit trigonometry graphs to learn the graphs of each of the functions in detail along with their maximum and minimum values and solved examples.

Also Check: Inverse Trigonometric Graphs

A frequency distribution graph is used to show the frequency of the outcomes in a particular sample. For frequency distribution graphs, the table of values made by placing the outcomes in one column and the number of times they appear (i.e. frequency) in the other column. This table is known as the frequency distribution table from which the cumulative frequency graph or ogive can be plotted.

There are two commonly used frequency graphs which include:

• Frequency Polygon
• Cumulative Frequency Distribution Graphs

More Topics Related to Graphs:

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• Data Structures
• Linked List
• Binary Tree
• Binary Search Tree
• Segment Tree
• Disjoint Set Union
• Fenwick Tree
• Red-Black Tree
• Advanced Data Structures
• Graph Data Structure And Algorithms
• Introduction to Graphs - Data Structure and Algorithm Tutorials

Graph and its representations

• Types of Graphs with Examples
• Basic Properties of a Graph
• Applications, Advantages and Disadvantages of Graph
• Transpose graph
• Difference Between Graph and Tree

BFS and DFS on Graph

• Breadth First Search or BFS for a Graph
• Depth First Search or DFS for a Graph
• Applications, Advantages and Disadvantages of Depth First Search (DFS)
• Applications, Advantages and Disadvantages of Breadth First Search (BFS)
• Iterative Depth First Traversal of Graph
• BFS for Disconnected Graph
• Transitive Closure of a Graph using DFS
• Difference between BFS and DFS

Cycle in a Graph

• Detect Cycle in a Directed Graph
• Detect cycle in an undirected graph
• Detect Cycle in a directed graph using colors
• Detect a negative cycle in a Graph | (Bellman Ford)
• Cycles of length n in an undirected and connected graph
• Detecting negative cycle using Floyd Warshall
• Clone a Directed Acyclic Graph

Shortest Paths in Graph

• How to find Shortest Paths from Source to all Vertices using Dijkstra's Algorithm
• Bellman–Ford Algorithm
• Floyd Warshall Algorithm
• Johnson's algorithm for All-pairs shortest paths
• Shortest Path in Directed Acyclic Graph
• Multistage Graph (Shortest Path)
• Shortest path in an unweighted graph
• Karp's minimum mean (or average) weight cycle algorithm
• 0-1 BFS (Shortest Path in a Binary Weight Graph)
• Find minimum weight cycle in an undirected graph

Minimum Spanning Tree in Graph

• Kruskal’s Minimum Spanning Tree (MST) Algorithm
• Difference between Prim's and Kruskal's algorithm for MST
• Applications of Minimum Spanning Tree
• Total number of Spanning Trees in a Graph
• Minimum Product Spanning Tree
• Reverse Delete Algorithm for Minimum Spanning Tree

Topological Sorting in Graph

• Topological Sorting
• All Topological Sorts of a Directed Acyclic Graph
• Kahn's algorithm for Topological Sorting
• Maximum edges that can be added to DAG so that it remains DAG
• Longest Path in a Directed Acyclic Graph
• Topological Sort of a graph using departure time of vertex

Connectivity of Graph

• Articulation Points (or Cut Vertices) in a Graph
• Biconnected Components
• Bridges in a graph
• Eulerian path and circuit for undirected graph
• Fleury's Algorithm for printing Eulerian Path or Circuit
• Strongly Connected Components
• Count all possible walks from a source to a destination with exactly k edges
• Euler Circuit in a Directed Graph
• Word Ladder (Length of shortest chain to reach a target word)
• Find if an array of strings can be chained to form a circle | Set 1
• Tarjan's Algorithm to find Strongly Connected Components
• Paths to travel each nodes using each edge (Seven Bridges of Königsberg)
• Dynamic Connectivity | Set 1 (Incremental)

Maximum flow in a Graph

• Max Flow Problem Introduction
• Ford-Fulkerson Algorithm for Maximum Flow Problem
• Find maximum number of edge disjoint paths between two vertices
• Find minimum s-t cut in a flow network
• Maximum Bipartite Matching
• Channel Assignment Problem
• Introduction to Push Relabel Algorithm
• Introduction and implementation of Karger's algorithm for Minimum Cut
• Dinic's algorithm for Maximum Flow

Some must do problems on Graph

• Find size of the largest region in Boolean Matrix
• Count number of trees in a forest
• A Peterson Graph Problem
• Clone an Undirected Graph
• Introduction to Graph Coloring
• Traveling Salesman Problem (TSP) Implementation
• Introduction and Approximate Solution for Vertex Cover Problem
• Erdos Renyl Model (for generating Random Graphs)
• Chinese Postman or Route Inspection | Set 1 (introduction)
• Hierholzer's Algorithm for directed graph
• Boggle (Find all possible words in a board of characters) | Set 1
• Hopcroft–Karp Algorithm for Maximum Matching | Set 1 (Introduction)
• Construct a graph from given degrees of all vertices
• Determine whether a universal sink exists in a directed graph
• Number of sink nodes in a graph
• Two Clique Problem (Check if Graph can be divided in two Cliques)

What is Graph Data Structure?

A Graph is a non-linear data structure consisting of vertices and edges. The vertices are sometimes also referred to as nodes and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph is composed of a set of vertices( V ) and a set of edges( E ). The graph is denoted by G(V, E) .

Representations of Graph

Here are the two most common ways to represent a graph :

Adjacency Matrix

Adjacency list.

An adjacency matrix is a way of representing a graph as a matrix of boolean (0’s and 1’s).

Let’s assume there are n vertices in the graph So, create a 2D matrix adjMat[n][n] having dimension n x n.

If there is an edge from vertex i to j , mark adjMat[i][j] as 1 . If there is no edge from vertex i to j , mark adjMat[i][j] as 0 .

Representation of Undirected Graph to Adjacency Matrix:

The below figure shows an undirected graph. Initially, the entire Matrix is ​​initialized to 0 . If there is an edge from source to destination, we insert 1 to both cases ( adjMat[destination] and adjMat [ destination]) because we can go either way.

Undirected Graph to Adjacency Matrix

Representation of Directed Graph to Adjacency Matrix:

The below figure shows a directed graph. Initially, the entire Matrix is ​​initialized to 0 . If there is an edge from source to destination, we insert 1 for that particular adjMat[destination] .

Directed Graph to Adjacency Matrix

An array of Lists is used to store edges between two vertices. The size of array is equal to the number of vertices (i.e, n) . Each index in this array represents a specific vertex in the graph. The entry at the index i of the array contains a linked list containing the vertices that are adjacent to vertex i .

Let’s assume there are n vertices in the graph So, create an array of list of size n as adjList[n].

adjList[0] will have all the nodes which are connected (neighbour) to vertex 0 . adjList[1] will have all the nodes which are connected (neighbour) to vertex 1 and so on.

Representation of Undirected Graph to Adjacency list:

The below undirected graph has 3 vertices. So, an array of list will be created of size 3, where each indices represent the vertices. Now, vertex 0 has two neighbours (i.e, 1 and 2). So, insert vertex 1 and 2 at indices 0 of array. Similarly, For vertex 1, it has two neighbour (i.e, 2 and 0) So, insert vertices 2 and 0 at indices 1 of array. Similarly, for vertex 2, insert its neighbours in array of list.

Undirected Graph to Adjacency list

Representation of Directed Graph to Adjacency list:

The below directed graph has 3 vertices. So, an array of list will be created of size 3, where each indices represent the vertices. Now, vertex 0 has no neighbours. For vertex 1, it has two neighbour (i.e, 0 and 2) So, insert vertices 0 and 2 at indices 1 of array. Similarly, for vertex 2, insert its neighbours in array of list.

Directed Graph to Adjacency list

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Title: haar graphical representations of finite groups and an application to poset representations.

Abstract: Let $R$ be a group and let $S$ be a subset of $R$. The Haar graph $\mathrm{Haar}(R,S)$ of $R$ with connection set $S$ is the graph having vertex set $R\times\{-1,1\}$, where two distinct vertices $(x,-1)$ and $(y,1)$ are declared to be adjacent if and only if $yx^{-1}\in S$. The name Haar graph was coined by Tomaž Pisanski in one of the first investigations on this class of graphs. For every $g\in R$, the mapping $\rho_g:(x,\varepsilon)\mapsto (xg,\varepsilon)$, $\forall (x,\varepsilon)\in R\times\{-1,1\}$, is an automorphism of $\mathrm{Haar}(R,S)$. In particular, the set $\hat{R}:=\{\rho_g\mid g\in R\}$ is a subgroup of the automorphism group of $\mathrm{Haar}(R,S)$ isomorphic to $R$. In the case that the automorphism group of $\mathrm{Haar}(R,S)$ equals $\hat{R}$, the Haar graph $\mathrm{Haar}(R,S)$ is said to be a Haar graphical representation of the group $R$. Answering a question of Feng, Kovács, Wang, and Yang, we classify the finite groups admitting a Haar graphical representation. Specifically, we show that every finite group admits a Haar graphical representation, with abelian groups and ten other small groups as the only exceptions. Our work on Haar graphs allows us to improve a 1980 result of Babai concerning representations of groups on posets, achieving the best possible result in this direction. An improvement to Babai's related result on representations of groups on distributive lattices follows.

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