Question

Find the mode for the following data: ($4$ and $5$)

Class	$0-7$	$7-14$	$14-21$	$21-28$	$28-35$	$35-42$	$42-49$	$49-56$
Area	$26$	$31$	$35$	$42$	$82$	$71$	$54$	$19$

Answer 1

$\Rightarrow$ Class interval $28-35$ have higher frequency.

$\Rightarrow$ Modal class $=28-35$

$\Rightarrow$ $l=28,f_0=42,f_1=82,f_2=71$ and $h=7$

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

$=28+\frac{82-42}{2\times 82-42-72-}\times 7$

$=28+\frac{40}{50}\times 7$

$=28+5.6$

$=33.6$