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Question
Calculate the median from the following data:
| Rent (in Rs.): | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 | 75 - 85 | 85 - 95 |
| No. of Houses: | 8 | 10 | 15 | 25 | 40 | 20 | 15 | 7 |
Solution
| Class interval | Frequency | Cumulative frequency |
| 15 - 25 | 8 | 8 |
| 25 - 35 | 10 | 18 |
| 35 - 45 | 15 | 33 |
| 45 - 55 | 25 | 58 |
| 55 - 65 | 40 | 98 |
| 65 - 75 | 20 | 118 |
| 75 - 85 | 15 | 133 |
| 85 - 95 | 7 | 140 |
| N = 140 |
Here N = 140
So, N/2 = 70
Thus, the cumulative frequency just greater than 70 is 98 and the corresponding class is 55 - 65.
Therefore, 55 - 65 is the median class.
Here, l = 55, f = 40, F = 58 and h = 10
We know that
Median `=l +{(N/2-F)/f}xxh`
`=55+{(70-58)/40}xx10`
`=55+(12xx10)/40`
`=55+120/40`
= 55 + 3
= 58
Hence, the median is 58.
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