Graphical Representation of Data
Last Updated :
23 Jul, 2025
Graphical Representation of Data is 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.
The branch is widely spread and has many real-life applications such as Business Analytics, demography, Astro statistics, and so on.
Graphical Representation of DataGraphics 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 a visualized form.
There are two ways of representing data,
- Tables
- 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.
Types of Graphical 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:
Line Graphs
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.
Example: Draw a line graph for the given data
Bar Graphs
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.
Example: Draw a bar graph for the given data
Histograms
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.
Example: Draw a Histogram for the given data
| x | 5 - 25 | 25 - 45 | 45 - 65 | 65 - 85 |
|---|
| y | 6 | 8 | 3 | 3 |
|---|
Read More:Histograph
Line Plot
It is a plot that displays data as points and checkmarks above a number line, showing the frequency of the point.
Example: Line Plot for the given data:
Number | Frequency |
|---|
1 | 2 |
2 | 3 |
3 | 1 |
4 | 2 |
5 | 0 |
Read More: Line Plot
Stem and Leaf Plot
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).
Example:
The data represented in the stem and leaf plot is as follows: 03, 11, 14, 21, 23, 26.
Read More: Stem and Leaf Plot
Box and Whisker Plot
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.
Read More: Box and Whisker Plot
Pie Chart
It is a type of graph which represents the data in the form of a circular graph. The circle is divided such that each portion represents a proportion of the whole.
Read More: Pie Chart
Graphical Representations used in Maths
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 about lines of thoughts of making graphs in maths:
- Value-Based or Time Series Graphs
- Frequency Based
Value-Based or Time Series Graphs
These graphs allow us to study the change of a variable clearer than another variable within a given interval of time. The variables can be anything. Time Series graphs study the change of variables 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.
Frequency Based
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
Principles of Graphical Representations
- 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.
Advantages and Disadvantages of Using Graphical System
Advantages
- 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
General Rules for Graphical Representation of Data
We should keep in mind some things while plotting and designing these graphs. The goal should be a better and clearer picture of the data. The following things should be kept in mind while plotting the above graphs:
- Whenever possible, the data source must be mentioned to 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 least, a suitable title should be chosen.
Frequency Polygon
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.
Solved Examples of Graphical Representation of Data
Question 1: What are different types of frequency-based plots?
Answer:
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.
| Advertising Channel | Expenditure (In Crores) |
|---|
| TV Advertisement | 2 |
| Radio | 1 |
| Facebook | 3 |
| Instagram | 3 |
| Printed Media | 1 |
Draw a bar graph for the following data.
Solution:
Steps:
- 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
Solution:
Steps:
- 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:
| x | [0 - 3] | [3 - 16] | [6 - 9] | [9 - 12] |
|---|
| y | 3 | 4 | 2 | 6 |
|---|
Solution:
Steps:
- Draw the class intervals on the x-axis and frequencies on the y-axis.
- Calculate the midpoint of each class interval.
| Class Interval | Mid Point | Frequency |
|---|
| 0 - 3 | 1.5 | 3 |
| 3 - 6 | 4.5 | 4 |
| 6 - 9 | 7.5 | 2 |
| 9 - 12 | 10.5 | 6 |
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.
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