Question

Find the mode for the following frequency distribution.

Class	$0-100$	$100-200$	$200-300$	$300-400$	$400-500$	$500-600$
Frequency	$64$	$62$	$77$	$62$	$66$	$54$

Answer 1

Modal class is the class with maximum frequency. The modal class here is $200-300$.

$l$ is the lower limit of modal class, so $l=200$

$h$ is the size of class interval, so $h=300-200=100$

$f_1$ is the frequency of modal class, so $f_1=77$

$f_0$ is the frequency of the class preceding the modal class, so $f_0=62$

$f_2$ is the frequency of the class succeeding the modal class, so $f_2=62$

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

$Mode=200+\frac{77-62}{2\left(72\right)-62-62}\times 100$

$Mode=200+\frac{15}{20}\times 100$

$Mode=200+75$

$Mode=275$

Hence the mode is $275$.