Find the mode for the following frequency distribution:

Observe that, from the given data:

The maximum class frequency, here, is 15 and the class corresponding to this frequency is 20 – 24.

So, this implies that,

Modal class = 20 – 24

Mode of such grouped frequency distribution is given by,

Where,

l = lower limit of the modal class = 20

f₀ = frequency of the class preceding the modal class = 7

f₁ = frequency of the modal class = 15

f₂ = frequency of the class succeeding the modal class = 1

c = size of class interval (the class intervals are same) = 4

∴ Substituting the values l = 20, f₀ = 7, f₁ = 15, f₂ = 1 and c = 4 in the formula of mode. We get

⇒

⇒

⇒

⇒

⇒ Mode = 20 + 1.45

⇒ Mode = 21.45

Thus, the mode is 21.45.