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Question
The following is the distribution of height of students of a certain class in a certain city:
| Height (in cm): | 160 - 162 | 163 - 165 | 166 - 168 | 169 - 171 | 172 - 174 |
| No. of students: | 15 | 118 | 142 | 127 | 18 |
Find the median height.
Solution
First we prepare the following cummulative table to compute the median.
| Height (in cm) | Frequency (f1) | Cumulative Frequency (c.f) |
| 160 - 162 | 15 | 15 |
| 163 - 165 | 118 | 133 |
| 166 - 168 | 142 | 275 |
| 169 - 171 | 127 | 402 |
| 172 - 174 | 18 | 420 |
| N = 420 |
Now, N = 420
`thereforeN/2=420/2=210`
Thus, the cumulative frequency just greater than 210 is 275 and the corresponding class is 166 - 168.
Therefore, 166 - 168 is the median class.
l = 166, f = 142, F = 133 and h = 2
We know that,
Median `=l+{(N/2-F)/f}xxh`
`=166+{(210-133)/142}xx2`
`=166+(77xx2)/142`
`=166+154/142`
= 166 + 1.08
= 167.08
Hence, the median height is approximately 167.1 cm.
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