The data obtained for 100 shops for their daily profit per shop are as follows:

Find the modal profit per shop.

Observe that, from the given data:

The maximum class frequency, here, is 27 and the class corresponding to this frequency is 200 – 300.

So, this implies that,

Modal class = 200 – 300

Mode of such grouped frequency distribution is given by,

Where,

l = lower limit of the modal class = 200

f₀ = frequency of the class preceding the modal class = 18

f₁ = frequency of the modal class = 27

f₂ = frequency of the class succeeding the modal class = 20

c = size of class interval (the class intervals are same) = 100

∴ Substituting the values l = 200, f₀ = 18, f₁ = 27, f₂ = 20 and c = 100 in the formula of mode. We get

⇒

⇒

⇒

⇒

⇒ Mode = 200 + 56.25

⇒ Mode = 256.25

Thus, the modal profit per shop is Rs. 256.25.