The document provides instructions on how to construct a frequency distribution for a set of data by determining the class interval size. It gives an example of marks obtained by 50 students ranging from 12 to 77. It shows how to find the number of classes, calculate the class interval size, and determine the class boundaries to organize the data into classes for the frequency distribution. It then provides two practice questions asking to draw the frequency distribution for additional data sets.

1. Construct Frequency Distribution

2. Construct a frequency distribution with the suitable class interval size of marks
obtained by 50 students of a class, which are given below:
23, 50, 38, 42, 63, 75, 12, 33, 26, 39, 35, 47, 43, 52, 56, 59, 64, 77, 15, 21, 51,
54, 72, 68, 36, 65, 52, 60, 27, 34, 47, 48, 55, 58, 59, 62, 51, 48, 50, 41, 57, 65,
54, 43, 56, 44, 30, 46, 67, 53

3. Solution:
Arrange the marks in ascending order as
12, 15, 21, 23, 26, 27, 30, 33, 34, 35, 36, 38, 39, 41, 42, 43, 43, 44, 46, 47, 47, 48, 48, 50, 50, 51,
51, 52, 52, 53, 54, 54, 55, 56, 56, 57, 58, 59, 59, 60, 62, 63, 64, 65, 65, 67, 68, 72, 75, 77
Minimum Value = 12
Maximum = 77
Range = Maximum Value – Minimum Value = 77−12
= 65
Number of Classes = 1+3.322logN
Number of Classes = 1+3.322log50
Number of Classes = 1+3.322(1.69897)
Number of Classes = 1+5.64
= 6.64 or 7
Approximately:
Class Interval Size (h) = RangeNo. of Classes = 657 = 9.3 or 10

5. To find the class boundaries, we take half of the difference between the
lower class limit of the 2nd class and the upper class limit of the 1st
class20−192=12=0.5. This value is subtracted from the lower class limit and
is added to the upper class limit to get the required class boundaries

6. So, finally count after tally:

7. • Practice Question 1: Draw the frequency distribution of following data and
complete all steps
31, 41, 46, 33, 44, 51, 56, 63, 71, 71, 62, 63, 54, 53, 51, 43, 36, 38, 54, 56, 66,
71, 74, 75, 46, 47, 59, 60, 61, 63.
Practice Question 2: Draw the frequency distribution of following data and
complete all steps
118, 123, 124, 125, 127, 128, 129, 130, 130, 133, 136, 138, 141, 142, 149,
150, 154.

8. • A survey was taken on Maple Avenue. In each of 20 homes, people were asked
how many cars were registered to their households. The results were recorded as
follows:
1, 2, 1, 0, 3, 4, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 1, 4, 0, 0
So, frequency distribution will be: