Find the mode for the following data:

Class	0-7	7-14	14-21	21-28	28-35	35-42	42-49	49-56
Frequency	26	31	35	42	82	71	54	19

Observe that, from the given data:

The maximum class frequency, here, is 82 and the class corresponding to this frequency is 28 – 35.

So, this implies that,

Modal class = 28 – 35

Mode of such grouped frequency distribution is given by,

Where,

l = lower limit of the modal class = 28

f₀ = frequency of the class preceding the modal class = 42

f₁ = frequency of the modal class = 82

f₂ = frequency of the class succeeding the modal class = 71

c = size of class interval (the class intervals are same) = 7

∴ Substituting the values l = 28, f₀ = 42, f₁ = 82, f₂ = 71 and c = 7 in the formula of mode. We get

⇒

⇒

⇒

⇒ Mode = 28 + 5.49

⇒ Mode = 33.49

Thus, the mode is 33.49