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Question
The maximum speeds, in km per hour, of 35 cars in a race are given as follows:
| Speed (km/h) | 85 – 100 | 100 – 115 | 115 – 130 | 130 – 145 |
| Number of cars | 5 | 8 | 13 | 9 |
Calculate the median speed.
Solution
| Speed (km/h) | Number of cars `(f)` |
Cumulative frequency `(c.f.)` |
| 85 – 100 | 5 | 5 |
| 100 – 115 | 8 | 13 |
| 115 – 130 | 13 | 26 |
| 130 –145 | 9 | 35 |
Here, N = 35
∴ `N/2 = 35/2` = 17.5
Cumulative frequency (c.f.) just greater than 17.5 is 26, belonging to class interval 115 – 130.
∴ Median class = 115 – 130
So, L = 115, h = 15, f = 13, cf. = 13.
Median = `L + ((N/2 - c.f.)/f) xx h`
= `115 + ((17.5 - 13)/13) xx 15`
= `115 + (4.5/13) xx 15`
= 115 + 5.192
= 120.192
Hence, the median speed of cars is 120.192 km/h.
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