Question

The following table gives the distribution of the life time of $400$ neon lamps:

Life time: (in hours)	Number of lamps
$1500-2000$	$14$
$2000-2500$	$56$
$2500-3000$	$60$
$3000-3500$	$86$
$3500-4000$	$74$
$4000-4500$	$62$
$4500-5000$	$48$

Find the median life.

Answer 1

Class interval	Frequency	Cumulative Frequency
$1500-2000$	$14$	$14$
$2000-2500$	$56$	$70$
$2500-3000$	$60$	$130$
$3000-3500$	$86$	$216$
$3500-4000$	$74$	$290$
$4000-4500$	$62$	$352$
$4500-5000$	$48$	$400$

We have, $N=400$ and $\frac{N}{2}=200$, hence median class is $3000-3500$.

So, $l=3000,cf=130,f=86$ and $h=500$

$Median=l+\frac{\frac{N}{2}-cf}{f}\times h$

$\Rightarrow$ $Median=3000+\frac{200-130}{86}\times 500$

$\Rightarrow$ $Median=3000+406.98=3406.98$