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Question
The median of the following frequency distribution is 25. Find the value of x.
| Class: | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency: | 6 | 9 | 10 | 8 | x |
Solution
| Class Interval | Frequency | Cumulative frequency (`"C"_f`) |
| 0 – 10 | 6 | 6 |
| 10 – 20 | 9 | 15 |
| 20 – 30 | 10 | 25 |
| 30 – 40 | 8 | 33 |
| 40 – 50 | x | 33 + x |
| `sumf_i` = 33 + x |
Total frequency = 33 + x
i.e., N = 33 + x
∴ `"N"/2 = (33 + x)/2`
Median = 25
So class corresponding to this 20 – 30,
So, l = 20, `"C"_f` = 15, `f` = 10 and h = 10
Median = `"l" + (("N"/2 - "c"_f)/f) xx "h"`
⇒ 25 = `20 + (((33 + x)/2 - 15)/10) xx 10`
⇒ 25 = `20 + (33 + x - 30)/2` ...[Given, Median = 25]
⇒ 25 – 20 = `(3 + x)/2`
⇒ 10 = 3 + x
⇒ x = 7
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