Question

The following table gives the distribution of the life time of 400 neon lamps:
$\begin{array}{cc}& \\ \text{Lite time}:\left(\text{in hours}\right)& \text{Number of lamps}\\ 1500-2000& 14\\ 2000-2500& 56\\ 2500-3000& 60\\ 3000-3500& 86\\ 3500-4000& 74\\ 4000-4500& 62\\ 4500-5000& 48\end{array}$
Find the median life.

Answer 1

Life time	Number of lamps $f_i$	Cumulative frequency (cf or F)
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
Total (N)	400

Now we may observe that cumulative frequency just greater than $\frac{N}{2}$ ($=\frac{400}{2}=200$) is 216 belongs to class interval 3000 – 3500

Median class = 3000 – 3500

Lower limits (l) of median class = 3000

Frequency (f) of median class = 86

Cumulative frequency (cf or F) of class preceding median class = 130

Class size (h) = 500

$Median=L+\frac{\frac{N}{2}-F}{f}\times h$

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

$=3000+\frac{35000}{86}=3406.98$

So, median life time of lamps is 3406.98 hours