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Question
If the median of the distribution given below is 28.5, find the values of x and y.
| Class interval | Frequency |
| 0 - 10 | 5 |
| 10 - 20 | x |
| 20 - 30 | 20 |
| 30 - 40 | 15 |
| 40 - 50 | y |
| 50 - 60 | 5 |
| Total | 60 |
Solution
The cumulative frequency for the given data is calculated as follows:
| 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 |
| Total (n) | 60 |
From the table, it can be observed that n = 60
45 + x + y = 60
x + y = 15 (1)
the median of the data is given as 28.5, which lies in the intervals 20 − 30.
Therefore, the median class is 20 − 30
lower limit (l) of the median class is 20
Cumulative frequency (cf) of class preceding the median class = 5 + x
Frequency (f) of median class = 20
Class size (h) = 10
Median = `l + (((n/2)-cf)/f)xxh`
`28.5 = 20 + [(60/2-(5+x))/20]xx10`
`8.5 = ((25-x)/2)`
17 = 25 − x
8 + y = 15
y = 7
Hence, the values of x and y are 8 and 7, respectively.
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