The marks obtained (out of 100) by a class of 80 students are given below :
Marks Number of students
10 - 20 6
20 - 30 17
30 - 50 15
50 - 70 16
70 - 100 26

Construct a histogram to represent the data above.

Solution:

Given, the table represents the frequency distribution of total marks obtained by a class of 80 students

We have to draw a histogram for the above distribution.

We observe that the class intervals of the frequency distribution are not of equal width.

We have to make modifications in the lengths of the rectangles in the histogram, so that the areas of rectangles are proportional to the frequencies.

Adjusted frequency of a class=(Minimum class size / Class size of that class) × Frequency of the class

Minimum class size = minimum class interval = 20 - 10 = 10

Marks	Frequency	Class interval	Length of the rectangle
10 - 20	6	10	(10/10) × 6 = 6
20 - 30	17	10	(10/10) × 17 = 17
30 - 50	15	20	(10/20) × 15 = 7.5
50 - 70	16	20	(10/20) × 16 = 8
70 - 100	26	30	(10/30) × 26 = 8.67

Now, draw the histogram with the following data

Marks	Adjusted Frequency
10 - 20	6
20 - 30	17
30 - 50	7.5
50 - 70	8
70 - 100	8.67

We can represent the class intervals of age along the horizontal axis.

The corresponding frequencies of the number of teachers are represented along the vertical axis.

Given, the interval start with 10 - 20

This implies that there is a break near the origin.

Using the given data, a histogram is given below,

✦ Try This: The marks obtained (out of 100) by a class of 80 students are given below :

Marks	Number of students
10 - 20	15
20 - 30	27
30 - 50	5
50 - 70	7
70 - 100	26

Construct a histogram to represent the data above.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

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NCERT Exemplar Class 9 Maths Exercise 14.4 Problem 6

The marks obtained (out of 100) by a class of 80 students are given below : Marks Number of students 10 - 20 6 20 - 30 17 30 - 50 15 50 - 70 16 70 - 100 26. Construct a histogram to represent the data above.

Summary:

A histogram for the class interval of marks and the corresponding frequencies of the number of students of a class is mentioned above

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