Q) The mode of the following frequency distribution is 55. Find the missing frequencies ‘a’ and ‘b’.

Ans: Since we know that, the modal class is the class with the highest frequency.

In the given data, class “45 – 60” has the highest frequency of 15.

Hence, class “45 – 60” is the modal class.

Now mode of the grouped data is calculated by:

x h

Here,

L = lower class limit of modal class

 = frequency of modal class

 = frequency of class proceeding to modal class

 = frequency of class succeeding to modal class.

h = class size,

Let’s put values, we get

x 15

x 15

10 (20-a) = (15 – a)15

5a = 25

a = 5

Next, we will take the total of all frequencies:

51 = 6 + 7 + a + 15 + 10 +  b

a + b = 51 – 38 = 13

Since a  = 5, hence, b = 8

Therefore, the values of a & b are 5 & 8 respectively.