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प्रश्न
Calculate the missing frequency from the following distribution, it being given that the median of distribution is 24.
| Class | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 - 50 |
| Frequency | 5 | 25 | ? | 18 | 7 |
उत्तर
| Class | Frequency (fi) | Cumulative Frequency (cf) |
| 0 – 10 | 5 | 5 |
| 10 – 20 | 25 | 30 |
| 20 – 30 | x | x+30 |
| 30 – 40 | 18 | x+48 |
| 40 – 50 | 7 | x+55 |
Median is 24 which lies in 20 – 30
∴ Median class = 20 – 30
Let the unknown frequency be x.
Here, l = 20, `n/2 = (x+55)/2`, c.f. of the preceding class = c.f = 30, f = x, h = 10
Now,
Median, `M = l + (n/2−cf)/f× h`
`⇒ 24 = 20 + (x+55/2 − 30)/x × 10`
`⇒ 24 = 20 + (x + 55 − 60/2)/ x × 10`
⇒ 24 = 20 +` (x−5 )/(2x) `× 10
⇒ 24 = 20 + `(5x−25)/ x`
⇒ 24 = 20+`( 5x−25)/ x`
⇒ 24x = 25x – 25
⇒ –x = – 25
⇒ x = 25
Hence, the unknown frequency is 25.
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