Question

The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.

No. of bulbs produced (Thousands)	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
No. of factories	$12$	$35$	$20$	$15$	$8$	$7$	$8$

Answer 1

$No.ofbulbsproduced$	$No.offactories$ $f$	$c.f.$
$30-40$	$12$	$12$
$40-50$	$35$	$47$
$50-60$	$20$	$67$
$60-70$	$15$	$82$
$70-80$	$8$	$90$
$80-90$	$7$	$97$
$90-100$	$8$	$105$
	$\sum f=105$

$\Rightarrow$ $\frac{N}{2}=\frac{105}{2}=52.5$

$\therefore$ Median class $=50-60$

So, $l=50,c.f=47,f=20$ and $h=10$

$\Rightarrow$ $Median=l+\frac{\frac{N}{2}-c.f}{f}\times h$

$=50+\frac{52.5-47}{20}\times 10$

$=50+2.75$

$=52.75$ thousand bulbs

$=52750$ bulbs.

Hence, the median of the production is $52750$ bulbs