Class 9 - Histogram: Definition, Graph & Solved Examples

A histogram is a way of graphically representing the distribution of numerical data. It organizes data into intervals and represents the frequency of data points in each interval using adjacent bars. A histogram helps to analyse big datasets into an understandable visual format. In a histogram, the continuous data is displayed through each bar that denotes a range of values. It is opposite to a bar graph which represents catagorical data. While they both look similar as they use vertical bars to represent data but they are fundamentally different. Let's understand in detail about the graphical representation of data using histogram and how are they different from bar graphs.
 

Table of Contents

• What is a Histogram
• How to Draw a Histogram
• Solved Examples on Histogram
• Practice Questions on Histogram

What is a Histogram

Histograms is a graphical representation of a grouped frequency distribution with continuous classes. Also, unlike a bar graph, the width of the bar plays a significant role in its construction.

How to Draw a Histogram

Understanding what a histogram is and how to define it leads to a clear process that produces an easy-to-understand histogram graph.

Use these steps to create a histogram: 
1. Gather and prepare the data: Compile numerical observations, either continuous or discrete. 
2. Define the range and the number of bins: Depending on the data spread, choose variable-width or uniform bin widths. 
3. Count frequencies: Tally the number of observations that fit into each bin.
4. Draw bars: Mark bins on the horizontal axis of the histogram graph. 
5. Plot frequency counts on the vertical axis. 
6. Title and label axes: Give your chart a title, clearly label the axes with the appropriate units, and, if you want, annotate the bars with frequencies.

 

Solved Examples on Histogram

Example 1: Draw a histogram for following class interval with frequency:

 

Solution: Draw histogram with X-axis as the height intervals and Y-axis representing the frequency. Bars should be adjacent to show continuity

Interpretation: The distribution is fairly symmetric, peaking around the 150-154 and 165-169 ranges. This is a great example of histogram for school-level analysis.

Example 2: A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she grouped them into intervals as: 0 - 20, 20 - 40, . . .,40 - 60, 60 -  80 and 80-100. Then she formed the following table:

Marks	Frequency
0-20	7
20-40	10
40-60	10
60-80	20
80-100	20

Draw a histrogram for the given table.

Solution: Draw a histogram with X-axis as the marks interval and Y-axis representing the frequency. Bars should be adjacent to show continuity as:

Practice Questions on Histogram

1. Plot histogram graph for the following table where X-axis represents the bill amount (₹) and Y-axis represents the number of houses
   Draw bars without gaps between them

2. Draw histogram for the following data: