QQuestion
The median of following data is 32. Find the value of x and y if x + y = 100.
| Class Interval | Frequency |
|---|---|
| 0 – 10 | 10 |
| 10 – 20 | x |
| 20 – 30 | 25 |
| 30 – 40 | 30 |
| 40 – 50 | y |
| 50 – 60 | 10 |
✓Answer
| Class Interval | Frequency (f) | CF |
|---|---|---|
| 0 – 10 | 10 | 10 |
| 10 – 20 | x | 10 + x |
| 20 – 30 | 25 | 10 + x + 25 |
| 30 – 40 | 30 | 10 + x + 25 + 30 |
| 40 – 50 | y | 10 + x + 25 + 30 + y |
| 50 – 60 | 10 | 100 |
Since x + y = 100, the total cumulative frequency at the last row must be 100.
Median class = 30 – 40.
Median = L + \left( \frac{\frac{n}{2} - CF}{f} \right) \times h
where:
- L = 30
- n = 100 (total frequency)
- CF = 35 + x
- f = 30
- h = 10
- Median = 32
Substituting values:
32 = 30 + \left( \frac{50 - (35 + x)}{30} \right) \times 10
or, 32 – 30 = \left( \frac{15 - x}{30} \right) \times 10
or, 2 = \frac{150 - 10x}{30}
or, 60 = 150 – 10x
or, 10x = 90
or, x = 9
Now, x + y = 100
or,9 + y = 100
y = 91
∴ x = 9 and y = 91
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