A graphical representation is a visual way to show data using shapes, lines, or symbols. It helps us understand the data quickly and easily by turning numbers into pictures. Instead of reading large amounts of numbers or information, we can look at a graph or chart and understand what is happening at a glance. This makes it easier to compare values, see patterns, or find trends. Graphical tools like bar graphs, pie charts, line graphs, and histograms are often used in maths and statistics to make data more meaningful. They also help in solving problems and making decisions based on the data shown. Graphs are very useful when we need to explain data clearly and simply, especially in classrooms, reports, or presentations. In short, graphical representation turns raw data into a clear and useful visual form.

What is Graphical Representation?

A graphical representation is a way of showing data or results using pictures, charts, or graphs instead of just using numbers or tables. It is often more effective and easier to understand than looking at a list of numbers. Graphs help us to see the relationship between different values clearly and quickly. They can show how one thing changes when another changes, which is useful when comparing or studying two variables.

Some common types of graphs used to show data include bar graphs, pie charts, line graphs, histograms, and scatter plots. Each type of graph is useful for showing different kinds of information in a neat and organized way. For example, a bar graph is good for comparing amounts, while a line graph is better for showing changes over time.

Using graphs makes it easier to spot trends, patterns, or differences in data. They can also help in finding important values like the mode or median. Overall, graphical representation is a helpful tool in maths and statistics. It allows us to understand data quickly, make comparisons, and draw conclusions in a simple visual way.

Data can be represented in different ways such as graphs, charts, plots etc. There are different types of graphical representations of data. Some of them are as follows:

• Bar Graph
• Pie Chart
• Line Graph
• Pictograph
• Histogram
• Frequency Distribution
• Stem and Leaf Plot
• Scatter Plot

1. Bar Graph: A bar graph is a pictorial representation of data in which bars of uniform width are drawn with equal spacing between them. The height of each bar depends on the values they represent.

Example: The given bar graph shows the number of matches played by different teams.

2. Pie Chart: A pie chart is a representation of values as slices of a circle with different colours. The slices are labelled and the numbers corresponding to each slice are also represented in the chart.

Example: The given figure is an example of the pie chart.

3. Line Graph: A line graph is a type of graph which is used to show information that changes over time. We can plot the line graph by joining several points with straight lines. A line graph is also called a line chart. A line graph contains two axes i.e., the x-axis and the y-axis.

Example: The given figure is an example of a line graph.

4. Pictograph: A way of graphing categorical data by using pictures to represent data items. In other words, pictographs are a way of representing statistical data using symbolic figures to match the frequencies of different kinds of data.

Example: The given figure is an example of a pictograph.

5. Histogram: The histogram is a type of graph that shows continuous data represented on a two-dimensional graph. In the histogram, the bars are placed side by side without a gap between consecutive bars. The histogram is a very popular method of presenting continuous series and class intervals.

Example: The given figure is an example of a histogram.

6. Frequency Distribution: A frequency distribution is a representation, either in graphical or tabular format, that displays the number of observations within a given interval. The interval must be mutually exclusive and exhaustive. Frequency distributions are typically used within a statistical context.

Example: The given figure is an example of frequency distribution.

7. Stem and Leaf Plot: A stem and leaf plot shows a large amount of data in a clear way by listing it in order of place value. A stem and leaf plot is generally used when the data has multi-digit numbers.

Stem – largest place value(s) of a number,

Leaf – smallest place value of a number

Example: In the given figure, the stem represents the tens digit and the leaves represent ones.

8. Scatter Plot: Scatter plots show many points plotted in the Cartesian plane. Each point represents the values of two variables. One variable is chosen on the horizontal axis and the other on the vertical axis.

Example: The given figure is an example of a scatter plot.

General Rules for Graphical Representation of Data

When you make a graph to show data, follow these basic rules to make it clear and easy to understand:

1.Give a Suitable Title

Your graph should have a clear title that tells what the graph is about.

2.Show Measurement Units

Always mention what units you're using — like cm, kg, or hours — so people know what the numbers mean.

3.Use a Proper Scale

Choose a scale (like 1 square = 10 students) that fits your data and makes the graph easy to read.

4.Add an Index or Key

If you use colours, patterns, or lines, add a key or legend to explain what they mean.

5.Mention the Data Source

If your data comes from a book, survey, or website, write the source below the graph (if needed).

6. Keep It Simple

Don’t make the graph too fancy. Keep it clean and easy for everyone to understand.

7. Make It Neat

Use the right size, colours, and labels. A neat graph is easier to read and looks better!

Importance of Graphical Representation of Data

1. Easy to Understand

Graphs make information simple to understand because they show facts and numbers in a clear way. We can remember them better since they grab our attention.

 2. Helps Compare Data

With graphs, we can easily compare different sets of data — like how something has changed over time.

3. Useful in Statistics

Graphs help in finding important statistical values like the mean (average), mode (most common), and median (middle value) of data.

4. Saves Time and Space

Graphs show a lot of information in a small space, using pictures or charts. This helps us understand the data quickly without reading long paragraphs.

Principle of Graphical Representation of Data

The principles of graphical representation of data are algebraic and are applicable to all types of it. In every graph, a data point is displayed using variables representing coordinate axes of the coordinate plane.

Coordinates are of two types, horizontal axes, and vertical axes, and they are placed perpendicular to each other with both the coordinates intersecting at the origin. The horizontal axis is known as X-axis and the vertical axis is known as Y-axis.

When the X-axis and Y-axis are intersected with each other at the origin it divides the coordinate plane into four parts which are called Quadrant I, Quadrant II, Quadrant III and Quadrant IV.

Following are some principles regarding the graphical representation of data given below:

• In the coordinate system, any point above the horizontal axis is taken as a positive value while any point below the horizontal axis is taken as a negative value.
• In the coordinate system, any point to the right of the vertical axis is taken as a positive value and any point to the left of the vertical axis is taken as a negative value.

General Rules for Graphical Representation

Following are a few rules to present the information in the graphical representation:

• The title of the graph should be appropriate that indicates the main subject of the presentation.
• The unit of measurement in the graph should be mentioned properly.
• Represent the data in an accurate manner with the help of proper scaling.
• To understand the graphical representation, index the appropriate colours, shades, lines and designs in graphs.
• Data sources should be included wherever it is necessary at the bottom of the graph.
• The construction of graphs should be in a simple way that everyone can understand.
• Always choose the correct size, fonts, colours, etc so that they should be a visual aid for presenting the information.

Advantages and Disadvantages of Graphical Representation

• Attractive and Impressive: Graphs are always more attractive and impressive than tables or figures.
• Simple and understandable presentation of data: Graphs help to present complex data in a simple and understandable way. It saves time and energy for both the statistician and the observer.
• Useful in comparison: Graphs provide an easy comparison of two or more phenomena.
• Location of positional averages: Grapha provides a method of locating certain positional averages like median, mode, quartiles, etc.
• Universal utility: Graphs can be used in all fields such as trade, economics, government departments, advertisements, etc.
• Helpful in predictions: Through graphs, tendencies that could occur in the near future can be predicted in a better way.

Disadvantages of Graphical Representation:

• Costly: Graphical representation of data is costly because it includes images, colours, and paints. A combination of human efforts and materials makes the graphical representation of data costly.
• Lack of Secrecy: Graphical representation of data makes the full presentation of information that may cause the objective of hiding something.
• Errors and Mistakes: There are more chances of errors in the graphical representation of data because it is complex. This will cause problems in a better understanding.
• More Time: Graphical representation of data takes more time in comparison to normal reports.

Uses of Graphical Representation of Data

• It helps us to relate and compare data for various time periods.
• It saves time as it covers most of the information in facts and figures.
• It is used in statistical analysis to determine the mean, median and mode for different data sets.
• It is easy for us to understand the graphical data as the information portrayed are in facts and figures.
• Data displayed by graphical representation can be memorised for the long term.
• The use of graphs in our daily life also helps in making and analysing.

Solved Examples of Graphical Representation

Example 1: Determine the following pair of equations has no solution, unique solution or infinitely many solutions using graphical method: 5x + 8y = -1, 3x – \(\frac{24}{5}\)y + \(\frac{3}{5}\) = 0.

Solution: From equation 5x + 8y = -1, we have

y = \(\frac{5x+1}{8}\)

And from equation 3x – \(\frac{24}{5}\)y + \(\frac{3}{5}\) = 0, we have

y = \(\frac{15x+3}{24}\)

Since the two lines coincide, the given system of equations will have infinitely many solutions.

Example 2: Solve the following system of equations graphically:

2x – y + 1 = 0 and x – 2y + 8 = 0.

Solution: From equation 2x – y + 1 = 0, we have

y = 2x + 1

And from equation x – 2y + 8 = 0, we have

y = \(\frac{x+8}{2}\)

There is exactly one point (2, 5) where the graph intersects. Hence, x = 2 and y = 5 is the only solution to the given system of equations.

We hope that the above article is helpful for your understanding and exam preparations. Stay tuned to the Testbook App for more updates on related topics from Mathematics, and various such subjects. Also, reach out to the test series available to examine your knowledge regarding several exams.