Question

A survey conducted on $20$ household in a locality by a group of statement resulted in the following frequency table for the number of family
Members in a house hold.

$\text{Family}\text{size}$	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$
$\text{Number}of\text{families}$	$7$	$8$	$2$	$2$	$1$

Find the mode of the data.

Answer 1

Family size	Number of families
$1-3$	$7=f_0$
$3-5$	$8=f_1$
$5-7$	$2=f_2$
$7-9$	$2$
$9-11$	$1$
	$\sum f=20$

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

Whereas,

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

$h=$ Class interval $=5-3=2$

$f_0=$ frequency of class preceeding the modal class $=7$

$f_1=$ frequency of modal class $=8$

$f_2=$ frequancy of class succeding the modal class $=2$

Therefore,

Mode $=3+\frac{8-7}{(2\times 8)-7-2}\times 2=3+\frac{1}{16-9}\times 2=3+\frac{2}{7}=3.286$

Hence the mode of the given data is $3.286$.