A survey conducted on 20 house holds in a locality resulted in the following frequency table.

What is the mode of this data?

$3\frac{2}{7}$

We know that,

Mode = l+ (f1- f0)/(2f1 - f0 - f2) × h

Here 

l = Lower limit of the modal class

f1 = Frequency of the modal class

f0 = Frequency of the previous modal class

f2 = Frequency of the after-modal class

h = size of the modal class

Here Range 3-5 has the highest frequency.

So, modal class = 3-5

l= 3, f0 = 7, f1 = 8, f2 = 2, h = 2

Mode = 3 + (8 - 7)/(2× 8 - 7 - 2) × 2

= 3 + 1/7 × 2

= 3 + 2/7

= 3 + 0.286 = 3.286 or $3\frac{2}{7}$