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Question
The median of the following frequency distribution is 35. Find the value of x.
| Class: | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency: | 6 | 3 | x | 12 | 19 |
Solution
| Class Interval |
Frequency | Cumulative frequency (`"C"_f`) |
| 0 – 10 | 6 | 6 |
| 10 – 20 | 3 | 9 |
| 20 – 30 | x | 9 + x |
| 30 – 40 | 12 | 21 + x |
| 40 – 50 | 19 | 40 + x |
| Total | `sumf_i` = 40 + x |
Total frequency = 40 + x
i.e., N = 40 + x
∴ `"N"/2 = (40 + x)/2`
Median = 35
∴ Median class = 30 – 40
Thus, l = 30, `"C"_f` = 9 + x, `f` = 12 and h = 10
Median = `l + ((N/2 - "C"_f)/f) xx "h"`
⇒ 35 = `30 + ({(40 + x)/2 - (9 + x)})/12 xx 10` ...[Given, median = 35]
⇒ 35 – 30 = `((22 - x) xx 10)/(2 xx 12)`
⇒ 5 = `((22 - x) xx 5)/12`
⇒ 12 = 22 – x
⇒ x = 10
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