Question

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

$\begin{array}{cc}\text{Life time}& \text{Number of lamps}\\ \text{(in hours)}& \\ 1500-2000& 14\\ 2000-2500& 56\\ 2500-3000& 60\\ 3000-3500& 86\\ 3500-4000& 74\\ 4000-4500& 62\\ 4500-5000& 48\end{array}$

Find the median life time of a lamp.

Answer 1

$\begin{array}{ccc}\text{Life time}& \text{Number of \& Cumulative}& \\ \text{(in hours)}& \text{lamps}& \text{Frequency}\\ 1500-2000& 14& 14\\ 2000-2500& 56& 70\\ 2500-3000& 60& 130\\ 3000-3500& 86& 216\\ 3500-4000& 74& 290\\ 4000-4500& 62& 352\\ 4500-5000& 48& 400\end{array}$

Now, n= 400

So, $\frac{n}{2}=\frac{400}{2}=200$

This observation lies in the class 3000-3500

So, 3000-3500 is the median class

Therefore, l = 3000, h = 500, cf = 130, f = 86

$\therefore Median=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h=3000+\left(\frac{200-130}{86}\right)\times 500$

$=3000+406.98=3406.98hours$

Hence, the median life time of a lamp is 3406.98 hours