Question :
| Class Interval | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | Total |
| Frequency | 5 | x | 20 | 15 | y | 5 | 60 |
Solution :
Here, it is given that median is 28.5
and n = 60
We now prepare the following cumulative frequency table :
| Class Interval | Frequency | Cumulative Frequency |
| 0 – 10 | 5 | 5 |
| 10 – 20 | x | 5 + x |
| 20 – 30 | 20 | 25 + x |
| 30 – 40 | 15 | 40 + x |
| 40 – 50 | y | 40 + x + y |
| 50 – 60 | 5 | 45 + x + y = 60 |
| Total | n = 60 |
Here, n = 60 So, \(n\over 2\) = 30
Since the median is given to be 28.5, thus the median class is (20 – 30).
\(\therefore\) l = 20, h = 10, f = 20 and cf = 5 + x
\(\therefore\) Median = l + (\({n\over 2} – cf\over f\)) \(\times\) h
\(\implies\) 28.5 = 20 + \(30 – (5 + x)\over 20\) \(\times\) 10
\(\implies\) 57 = 40 + 28 – x \(\implies\) x = 65 – 57 = 8
Also, 45 + x + y = 60
So, y = 7
Hence, x = 8 and y = 7.
