Question 2
If the median of a distribution given below is 28.5, 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 |
Solution:
Given data, n = 60
Median of the given data = 28.5
| CI | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50- 60 |
| Frequency | 5 | x | 20 | 15 | y | 5 |
| Cumulati ve frequency | 5 | 5+x | 25+x | 40+x | 40+x+y | 45+x+y |
Where, $\dfrac{N}{2}$ = 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 =$l+\dfrac{(\dfrac{N}{2})-cf}{f}\times h$ |
Substitute the values
28.5 = 20 + $[\dfrac{(30 − 5 − x)}{20}]$ × 10
8.5 = $\dfrac{(25 – x)}{2}$
17 = 25 – x
Therefore, x = 8
Now, from cumulative frequency, we can identify the value of x + y as follows:
Since,
60 = 45 + x + y
Now, substitute the value of x, to find y
60 = 45 + 8 + y
y = 60 – 53
y = 7
Therefore, the value of x = 8 and y = 7