graphical representation mathematics definition

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

go to slide go to slide

Book a Free Trial Class

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.

• Math Article

Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ideas, information and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

• Line Graphs – Line graph or the linear graph is used to display the continuous data and it is useful for predicting future events over time.
• Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
• Histograms – The graph that uses bars to represent the frequency of numerical data that are organised into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
• Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
• Frequency Table – The table shows the number of pieces of data that falls within the given interval.
• Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered with 100% and the categories occupied is represented with that specific percentage like 15%, 56%, etc.
• Stem and Leaf Plot – In the stem and leaf plot, the data are organised from least value to the greatest value. The digits of the least place values from the leaves and the next place value digit forms the stems.
• Box and Whisker Plot – The plot diagram summarises the data by dividing into four parts. Box and whisker show the range (spread) and the middle ( median) of the data.

General Rules for Graphical Representation of Data

There are certain rules to effectively present the information in the graphical representation. They are:

• Suitable Title: Make sure that the appropriate title is given to the graph which indicates the subject of the presentation.
• Measurement Unit: Mention the measurement unit in the graph.
• Proper Scale: To represent the data in an accurate manner, choose a proper scale.
• Index: Index the appropriate colours, shades, lines, design in the graphs for better understanding.
• Data Sources: Include the source of information wherever it is necessary at the bottom of the graph.
• Keep it Simple: Construct a graph in an easy way that everyone can understand.
• Neat: Choose the correct size, fonts, colours etc in such a way that the graph should be a visual aid for the presentation of information.

Graphical Representation in Maths

In Mathematics, a graph is defined as a chart with statistical data, which are represented in the form of curves or lines drawn across the coordinate point plotted on its surface. It helps to study the relationship between two variables where it helps to measure the change in the variable amount with respect to another variable within a given interval of time. It helps to study the series distribution and frequency distribution for a given problem.  There are two types of graphs to visually depict the information. They are:

• Time Series Graphs – Example: Line Graph
• Frequency Distribution Graphs – Example: Frequency Polygon Graph

Principles of Graphical Representation

Algebraic principles are applied to all types of graphical representation of data. In graphs, it is represented using two lines called coordinate axes. The horizontal axis is denoted as the x-axis and the vertical axis is denoted as the y-axis. The point at which two lines intersect is called an origin ‘O’. Consider x-axis, the distance from the origin to the right side will take a positive value and the distance from the origin to the left side will take a negative value. Similarly, for the y-axis, the points above the origin will take a positive value, and the points below the origin will a negative value.

Generally, the frequency distribution is represented in four methods, namely

• Smoothed frequency graph
• Pie diagram
• Cumulative or ogive frequency graph
• Frequency Polygon

Merits of Using Graphs

Some of the merits of using graphs are as follows:

• The graph is easily understood by everyone without any prior knowledge.
• It saves time
• It allows us to relate and compare the data for different time periods
• It is used in statistics to determine the mean, median and mode for different data, as well as in the interpolation and the extrapolation of data.

Example for Frequency polygonGraph

Here are the steps to follow to find the frequency distribution of a frequency polygon and it is represented in a graphical way.

• Obtain the frequency distribution and find the midpoints of each class interval.
• Represent the midpoints along x-axis and frequencies along the y-axis.
• Plot the points corresponding to the frequency at each midpoint.
• Join these points, using lines in order.
• To complete the polygon, join the point at each end immediately to the lower or higher class marks on the x-axis.

Draw the frequency polygon for the following data

Mark the class interval along x-axis and frequencies along the y-axis.

Let assume that class interval 0-10 with frequency zero and 90-100 with frequency zero.

Now calculate the midpoint of the class interval.

Using the midpoint and the frequency value from the above table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

To obtain the frequency polygon ABCDEFGHIJ, draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ, and connect all the points.

Frequently Asked Questions

What are the different types of graphical representation.

Some of the various types of graphical representation include:

• Line Graphs
• Frequency Table
• Circle Graph, etc.

Read More:  Types of Graphs

What are the Advantages of Graphical Method?

Some of the advantages of graphical representation are:

• It makes data more easily understandable.
• It saves time.
• It makes the comparison of data more efficient.

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Very useful for understand the basic concepts in simple and easy way. Its very useful to all students whether they are school students or college sudents

Thanks very much for the information

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

• Maths Notes Class 9
• NCERT Solutions Class 9
• RD Sharma Solutions Class 9
• Maths Formulas Class 9
• Class 9 Syllabus
• Class 9 Revision Notes
• Physics Notes Class 9
• Chemistry Notes Class 9
• Biology Notes Class 9
• History Notes class 9
• Geography Notes class 9
• Social science Notes class 9

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.

Similar Reads

• Mathematics
• School Learning
• Maths-Class-9

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

Talk to our experts

1800-120-456-456

• 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.   

All Subjects

Intro to Mathematical Analysis

Study guides for every class, that actually explain what's on your next test, graphical representation, from class:.

Graphical representation refers to the visual display of data or mathematical concepts using graphs, charts, or plots. This approach allows for a clearer understanding of relationships between variables, making complex information more digestible and highlighting key features such as maximum and minimum values.

congrats on reading the definition of Graphical Representation . now let's actually learn it.

5 Must Know Facts For Your Next Test

• Graphical representations are essential for visualizing functions to identify local and global extrema effectively.
• The Extreme Value Theorem states that a continuous function on a closed interval must attain both a maximum and minimum value, which can be shown through its graphical representation.
• In graphical representation, turning points of a function indicate potential local maxima and minima, helping to visualize where these extreme values occur.
• By plotting a function's graph, you can easily see the overall behavior of the function, including intervals of increase and decrease, which relate to finding extrema.
• Understanding graphical representations aids in interpreting the implications of the Extreme Value Theorem in real-world contexts, such as optimization problems.

Review Questions

• Graphical representation makes it easier to visualize how a continuous function behaves on a closed interval, illustrating where maximum and minimum values occur. By plotting the function, one can observe turning points that signify potential local extrema. This visual aid helps reinforce the idea that every continuous function on a closed interval must reach its highest and lowest values, as stated by the theorem.
• Identifying local extrema is crucial because it helps in understanding the overall behavior of functions represented graphically. Local maxima and minima give insight into trends and changes in direction within the graph. Recognizing these points enables us to apply the Extreme Value Theorem effectively, confirming that the function attains its highest and lowest values on specified intervals, which is vital for optimization.
• Graphical representation significantly enhances problem-solving strategies by providing a visual context for understanding relationships between variables in real-world scenarios. For example, when optimizing production costs or maximizing profits, visualizing these functions helps identify critical points where maximum efficiency occurs. This approach not only illustrates theoretical concepts like those in the Extreme Value Theorem but also translates them into actionable insights that guide decision-making in practical applications.

Related terms

Function : A mathematical relation where each input is associated with exactly one output, often represented as a graph in the Cartesian plane.

Local Extrema : Points in a function where the value is higher or lower than all nearby points, crucial for identifying the maximum and minimum values.

A function that is uninterrupted and has no breaks, jumps, or holes in its graph over a given interval.

" Graphical Representation " also found in:

Subjects ( 19 ).

• AP Computer Science A
• AP Human Geography
• Advanced Communication Research Methods
• Bioinformatics
• College Algebra
• College Introductory Statistics
• Computational Mathematics
• Elementary Algebra
• Fractal Geometry
• Honors Algebra II
• Honors Biology
• Honors Statistics
• Introduction to Directing
• Introduction to Mathematical Economics
• Market Research: Tools and Techniques for Data Collection and Analysis
• Mathematical Modeling
• Mathematical Tools for the Physical Sciences
• Stage Management
• Statics and Strength of Materials

© 2024 Fiveable Inc. All rights reserved.

Ap® and sat® are trademarks registered by the college board, which is not affiliated with, and does not endorse this website..