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Question
Calculate the median from the following data:
| Height(in cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 | 155 - 160 | 160 - 165 | 165 - 170 | 170 - 175 |
| Frequency | 6 | 10 | 18 | 22 | 20 | 15 | 6 | 3 |
Solution
| Class | Frequency (f) | Cumulative Frequency (cf) |
| 135 – 140 | 6 | 6 |
| 140 – 145 | 10 | 16 |
| 145 – 150 | 18 | 34 |
| 150 – 155 | 22 | 56 |
| 155 – 160 | 20 | 76 |
| 160 – 165 | 15 | 91 |
| 165 – 170 | 6 | 97 |
| 170 – 175 | 3 | 100 |
| N = Σ𝑓 = 100 |
Now, N = 100
`⇒ N/2` = 50.
The cumulative frequency just greater than 50 is 56 and the corresponding class is 150 - 155.
Thus, the median class is 150 – 155.
∴ l = 150, h = 5, f = 22, cf = c.f. of preceding class = 34 and `N/2` = 50.
Now,
Median, `M = l + {h×((N/2−cf)/f)}`
`= 150 + {5 × ((50 − 34)/22)}`
= 150 + 3.64
= 153.64
Hence, the median = 153.64.
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