Find the mode of the following frequency distribution:

Observe that, from the given data:

The maximum class frequency, here, is 86 and the class corresponding to this frequency is 3000 – 3500.

So, this implies that,

Modal class = 3000 – 3500

Mode of such grouped frequency distribution is given by,

Where,

l = lower limit of the modal class = 3000

f₀ = frequency of the class preceding the modal class = 60

f₁ = frequency of the modal class = 86

f₂ = frequency of the class succeeding the modal class = 74

c = size of class interval (the class intervals are same) = 500

∴ Substituting the values l = 3000, f₀ = 60, f₁ = 86, f₂ = 74 and c = 500 in the formula of mode. We get

⇒

⇒

⇒

⇒

⇒ Mode = 3000 + 342.10

⇒ Mode = 3342.10

Thus, the mode of the data is 3342.10.