If the median of the distribution is 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 |
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)
Median of the data is given as 28.5 which lies in interval 20 − 30.
Therefore, median class = 20 − 30
Lower limit (l) of median class = 20
Cumulative frequency (cf) of class preceding the median class = 5 + x
Frequency (f) of median class = 20
Class size (h) = 10
From equation (1),
8 + y = 15
y = 7
Hence, the values of x and y are 8 and 7 respectively.