Find the mode of the following frequency distribution:

Class	0-15	15-30	30-45	45-60	60-75	75-90	90-105
Frequency	8	16	23	57	33	23	13

Observe that, from the given data:

The maximum class frequency, here, is 57 and the class corresponding to this frequency is 45 – 60.

So, this implies that,

Modal class = 45 – 60

Mode of such grouped frequency distribution is given by,

Where,

l = lower limit of the modal class = 45

f₀ = frequency of the class preceding the modal class = 23

f₁ = frequency of the modal class = 57

f₂ = frequency of the class succeeding the modal class = 33

c = size of class interval (the class intervals are same) = 15

∴ Substituting the values l = 45, f₀ = 23, f₁ = 57, f₂ = 33 and c = 15 in the formula of mode. We get

⇒

⇒

⇒

⇒

⇒ Mode = 45 + 8.793

⇒ Mode = 53.793

Thus, the mode of the data is 53.793.