Find the mode of the following data:

Observe that, from the given data:

The maximum class frequency, here, is 28 and the class corresponding to this frequency is 50 – 60.

So, this implies that,

Modal class = 50 – 60

Mode of such grouped frequency distribution is given by,

Where,

l = lower limit of the modal class = 50

f₀ = frequency of the class preceding the modal class = 17

f₁ = frequency of the modal class = 28

f₂ = frequency of the class succeeding the modal class = 23

c = size of class interval (the class intervals are same) = 10

∴ Substituting the values l = 50, f₀ = 17, f₁ = 28, f₂ = 23 and c = 10 in the formula of mode. We get

⇒

⇒

⇒

⇒ Mode = 50 + 6.875

⇒ Mode = 56.875

Thus, the mode of the data is 56.875.