Let us find the mode of frequency distribution table given below :

[Hints : In the case of finding mode, we take lower limit of modal class, so we first correct the class limit in inclusive form of class limit.]

This is a grouped frequency distribution table which is inclusive type.

We need to convert this inclusive type of data into exclusive type of data to find mode of these data values.

To convert to exclusive type of data, subtract 0.5 from the lower class of the interval and add 0.5 to the upper class of the interval.

Notice the greatest frequency is 32.

⇒ Modal class = 74.5 – 84.5

Mode is given by

Where,

L = Lower class limit of the modal class = 74.5

h = class interval of the modal class = 10

f₁ = frequency of the modal class = 32

f₀ = frequency of the class preceding the modal class = 19

f₂ = frequency of the class succeeding the modal class = 12

Substituting values in the formula of mode,

⇒

⇒

⇒ Mode = 74.5 + 3.94

⇒ Mode = 78.44

Thus, mode is 78.44.