Question

Find the mode of given data.

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$20$	$24$	$40$	$36$	$20$

Answer 1

We use a formula to find mode of continuous data.

Mode $=x_1+\frac{f_0-f_1}{2f_0-f_1-f_{-1}}\times w$

$x_i=$ lower class of modal class

$f_0=$ frequency of modal class.

$f_1=$ frequency of class next to modal class

$f_{-1}=$ frequency of class previous to modal class

$w=$ width of modal class

Max freq $=40\therefore$ Modal class $=20-30$

$x_i=20$

$f_0=40$

$f_1=24$

$f_{-1}=36$

$w=10$

$\therefore$ mode $=20+\frac{40-24}{2\left(40\right)-24-36}\times 10$

$=20+\frac{16}{20}\times 10$

$=28$

$\therefore$ Mode $=28$