Question

Calculate the mode for the following data $:$

Weight	$45-55$	$55-65$	$65-75$	$75-85$	$85-95$
Number of persons	$1$	$2$	$3$	$10$	$7$

• A. $80$
• B. $81$
• C. $82$
• D. $83$

Answer 1

Answer: (C)

$82$

Here frequency of class interval $75-85$ is maximum.

So, it is the modal class

Now $l$ = lower limit of modal class $=75$

$f_1=$ frequency of modal class$=10$

$f_0=$frequency of class preceding the modal class $=3$

$f_2=$ frequency of class succeeding the modal class $=7$

$h=$ class interval width $=10$

So, Mode $=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

$=75+\left(\frac{10-3}{2\times 10-3-7}\right)\times 10$

$=75+\left(\frac{7}{20-10}\right)\times 10$

$=75+7$

$=82$

Mode$=82$