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Question
Find the median of the following frequency distribution:
| Class: | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 |
| Frequency: | 6 | 8 | 5 | 9 | 7 |
Solution
| Class Interval | Frequency | Cumulative frequency (cf) |
| 0 – 20 | 6 | 6 |
| 20 – 40 | 8 | 14 |
| 40 – 60 | 5 | 19 |
| 60 – 80 | 9 | 28 |
| 80 – 100 | 7 | 35 |
| N = `sumf_i` = 35 |
Here, N = 35
⇒ `"N"/2 = 35/2`
So, Median class is 40 – 60
Lower limit of median class (l) = 40
Class width (h) = 20
Frequency of median class (f) = 5
Precceding cf of median class (`"C"_f`) = 14
∴ Median = `l + ((N/2 - "C"_f)/f) xx h`
= `40 + ((35/2 - 14)/5) xx 20`
= 40 + 7 × 2
= 54
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