Question

Find 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 time of a lamp.

Answer 1

The cumulative frequencies with their respective class intervals are as follows.

Life time	Number of lamps (fi)	Cumulative frequency
1500 − 2000	14	14
2000 − 2500	56	14 + 56 = 70
3000 − 3500	60	70 + 60 = 130
3000 − 3500	86	130 + 86 = 216
3500 − 4000	74	216 + 74 = 290
4000 − 4500	62	290 + 62 = 352
4500 − 5000	48	352 + 48 = 400
Total (n)	400

It can be observed that the cumulative frequency just greater than  `n/2 (i.e 400/2 = 200)` is 216

belonging to class interval 3000 − 3500.

Median class = 3000 − 3500

Lower limit (l) of median class = 3000

Frequency (f) of median class = 86

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

Class size (h) = 500

Median = `l +((n/2 -cf)/f)xxh`

= `3000+ ((200-130)/86)xx500`

= `3000+(70xx500)/86`

= 3406.976

Therefore, the median life time of lamps is 3406.98 hours.