Question

Family size	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$
No. of families	$14$	$16$	$4$	$4$	$2$

A survey conducted on $40$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household -
Find the mode of this data

• A. $3.29$
• B. $4.12$
• C. $2.56$
• D. $6.12$

Answer 1

The correct option is A $3.29$

Here the maximum class frequency is $16$, and the class corresponding to this frequency is $3-5$. So, the modal class is $3-5$.

Now, in the modal class $3-5$, lower limit of the modal class is $\left(l\right)=3$,

class size $\left(h\right)=$ 2, frequency of the modal class $\left(f_1\right)=16$,

frequency of class preceding the modal class $\left(f_0\right)=14$,

frequency of class succeeding the modal class $\left(f_2\right)=4$,

Substituting these values in the formula, we have
$Mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

$=3+\left(\frac{16-14}{2\times 16-14-4}\right)\times 2=3+\left(\frac{2}{14}\right)\times 2=3+\frac{4}{14}=3.29$