Question

The height of 20 students of a class (cm) are as given:
$132, 131, 135, 136, 134, 132, 131, 142, 142, 152, 151, 151, 148, 145, 132, 142, 156, 155, 152$ Arrange the data in the form of a table of grouped data frequency distribution.

Answer 1

Hint:
Here we have to find the table of grouped data frequency distribution. For that, we will first find the minimum value of height from the given data and the maximum value of height from the given data.
We will compute their range then, which will be equal to the difference of the largest value and the smallest value of height. We will select the desired number of classes and then we will find the class range by dividing the difference of largest and smallest value by the number of classes. Then we will form the table and arrange the data with desired frequency.

Complete step by step solution:
Let’s first find the minimum and maximum value of height from the given data.
Maximum height $=131cm$
Minimum height $=156cm$
Now, we will calculate their range.
Range $156-131=25$
The desired number of classes is 4
We will calculate class range now, which is equal to the ratio of range to the number of classes.
$\text{class range}=\dfrac{25}{4}=6.25\approx 6$
We will arrange the classes starting with the minimum value and of class interval 6.
Let’s draw the frequency distribution table with desired frequency of each class intervals:-

CLASS INTERVAL	FREQUENCY
131-137	9
137-143	3
143-149	2
149-155	4
155-161	2

Hence, this is the required table of frequency distribution.

Note:
Since we have drawn the frequency distribution table for the given data. We need to know its meaning and proper definition. A frequency distribution is defined as a tabular representation of data that represents the number of observations within a given class interval. The class intervals should always be mutually exclusive. Frequency distribution is used for summarizing and for getting overview of categorical data.