(Q7) The following table gives the distribution of the life-time of 400 neon lamps.

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

Find the median life-time of a lamp.

Answer :

Class Interval Frequency c.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
- n = ∑fi = 400 -

Total observations are n =

n
2
 th observation i.e.,
2
 =

200 lies in the class 3000-3500

∴ Median class = 3000 - 3500

Lower boundary l =

frequency of the median class f = 86

c.f = 130; Class size, h = 500

Median = l +
(
n
2
 - cf )
f
 × h
Median = +
-
86
 ×
Median = +
86
 ×

= .98

∴ Median life ≃ .98 hours