Question

The mode of the following data is 36. Find the missing frequency $\chi$ in it.

CLASS	0-10	10-20	20-30	30-40	40-50	50-60	60-70
FREQUENCY	8	10	$\chi$	16	12	6	7

Answer 1

$\Rightarrow$ Modal class $=30-40$

So, $f_0=x,f_1=16,f_2=12,l=30$ and $h=10$

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

$\Rightarrow$ $36=30+\frac{16-x}{2\times 16-x-12}\times 10$

$\Rightarrow$ $6=\frac{16-x}{20-x}\times 10$

$\Rightarrow$ $120-6x=160-10x$

$\Rightarrow$ $4x=40$

$\therefore$ $x=10$