If the median of a distribution given below is 28.5 then, find the value of x & y.
Class Interval - Frequency
0-10 → 5
10-20 → x
20-30 → 20
30-40 → 15
40-50 → y
50-60 → 5
Total → 60
Given data, n = 60
Median of the given data = 28.5
Where, n/2 = 30
Median class is 20 – 30 with a cumulative frequency = 25 + x
Lower limit of median class, l = 20
Cf = 5 + x
f = 20 & h = 10
Median = \(l + (\frac{\frac{n}{2} - C_f}{f}) \times h \)
Substitute the values
28.5 = 20 + ((30 − 5 − x)/20) × 10
8.5 = (25 – x)/2
17 = 25-x
Therefore, x =8
Now, from cumulative frequency, we can identify the value of x + y as follows:
60 = 5 + 20 + 15 + 5 + x + y
Now, substitute the value of x, to find y
60 = 5 + 20 + 15 + 5 + 8 + y
y = 60 - 53
y = 7
Therefore, the value of x = 8 and y = 7.