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 45
2500-3000 60
3000-3500 86
3500-4000 74
4000-4500 62
4500-5000 48
Find the median life time of a lamp.

Based on the given information, we can prepare the table shown above.
Here, we have, n=400 → n/2=200
The cumulative frequency just greater than n/2 is 216 and the corresponding class is 3000-3500.
Thus, 3000-3500 is the median class such that n/2=200, l=3000, cf=130, f=86, and h=500
We know that,
Median, M = l + \frac{\frac{n}{2} - cf}{f} \times h
Where,
l → lower limit of the median class
n → total number of observations (Σf)
cf → cumulative frequency of the class preceding the median class
f → frequency of the median class
h → class width
Substituting the corresponding values in the formula, we get:
M = 3000 + \frac{200 - 130}{86} \times 500
→ M = 3000 + \frac{70}{86} \times 500 = 3000 + 406.98 = 3406.98
Hence, median life time of a lamp is 3406.98 hours.