Find the mode for the following data:

Class	0-20	20-40	40-60	60-80	80-100	100-120	120-140	140-160	160-180
Frequency	11	14	18	21	31	27	12	11	10

Observe that, from the given data:

The maximum class frequency, here, is 31 and the class corresponding to this frequency is 80 – 100.

So, this implies that,

Modal class = 80 – 100

Mode of such grouped frequency distribution is given by,

Where,

l = lower limit of the modal class = 80

f₀ = frequency of the class preceding the modal class = 21

f₁ = frequency of the modal class = 31

f₂ = frequency of the class succeeding the modal class = 27

c = size of class interval (the class intervals are same) = 20

∴ Substituting the values l = 80, f₀ = 21, f₁ = 31, f₂ = 27 and c = 20 in the formula of mode. We get

⇒

⇒

⇒

⇒

⇒ Mode = 80 + 14.29

⇒ Mode = 94.29

Thus, the mode is 94.29