Question

A survey conducted on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:

$\begin{array}{cccccc}\text{FAMILY SIZE}& 1-3& 3-5& 5-7& 7-9& 9-1\\ \text{NUMBER}& 7& 8& 2& 1& 2\\ \text{OF FAMILIES}& & & & & \end{array}$

Find the mode of the data.

Answer 1

$\begin{array}{cccccc}\text{FAMILY SIZE}& 1-3& 3-5& 5-7& 7-9& 9-1\\ \text{NUMBER}& 7& 8& 2& 1& 2\\ \text{OF FAMILIES}& & & & & \end{array}$

Maximum class frequency is $8$ and the class corresponding to this frequency is $3-5.$

Modal class $=3-5$

$l=$ Lower limit of modal class $=3$

Class size (h) $=5-3=2$

Frequency of modal class $\left(f_1\right)=8$

Frequency of preceding class $\left(f_0\right)=7$

Frequency of succeeding class $\left(f_2\right)=2$

We know that mode is given by

Mode = $l+\frac{(f_1-f_0)}{(2f_1-f_0-f_2)}h$

$=3+\frac{8-7}{2\times 8-7-2}\times 2$

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