Question :
| 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 |
Solution :
First, we prepare the following table to compute the median :
| Life time (in hours) | Number of lamps | Cumulative 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 |
We have : n = 400 So, \(n\over 2\) = 200
The cumulative frequency just greater than \(n\over 2\) is 216 and the corresponding class is (3000 – 3500). Thus, it is the median class.
Here, l = 3000, cf = 130, f = 86 and h = 500.
Substituting these values in the formula,
Median = l + (\({n\over 2} – cf\over f\))\(\times\)h, we have :
Median = 3000 + \(70\over 86\) \(\times\) 500 = 3000 + 406.98 = 3406.98
Hence, median life time is 3406.98 hours.
