Q) Find the mode of the following frequency distribution:

Ans: Since the modal class is the class with the highest frequency.

In the given question, class “40 – 50” has 17 frequency which is the highest frequency among all other classes.

Hence, modal class is “40 – 50”.

Now mode of the grouped data is calculated by:

Mode = L + x h

Here,

L = lower class limit of modal class = 40

 = frequency of modal class = 17

 = frequency of class proceeding to modal class = 12

 = frequency of class succeeding to modal class = 4

h = class size = 50 – 40 = 10

Let’s put values in the formula and solve:

Mode = L + x h

= 40 + x 10

= 40 + x 10

= 40 +   = 40 + 2    = 42

Hence, the mode value is 42

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