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प्रश्न
The median of the following distribution is 137. Find the values of x and y.
| Class | Frequency |
| 65 – 85 | 4 |
| 85 – 105 | 5 |
| 105 – 125 | x |
| 125 – 145 | 20 |
| 145 – 165 | 14 |
| 165 – 185 | y |
| 185 – 205 | 4 |
| Total | 68 |
योग
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उत्तर
Given that Median = 137
| Class | Frequency | Cumulative Frequency (cf) |
| 65 – 85 | 4 | 4 |
| 85 – 105 | 5 | 9 |
| 105 – 125 | x | 9 + x |
| 125 – 145 | 20 | 29 + x |
| 145 – 165 | 14 | 43 + x |
| 165 – 185 | y | 43 + x + y |
| 185 – 205 | 4 | 47 + x + y |
| Total | 68 = 47 + x + y |
Median = `l + ((n/2 - cf))/f xx h`
Median class = 125 – 145
l = 125, `N/2 = 68/2 = 34`, cf = 9 + x
f = 20, h = 20
Medain = `l + ((n/2 - cf))/f xx h`
`137 = 125 + ((34 - (9 + x)))/20 xx 20`
137 – 125 = 34 – (9 + x)
12 = 34 – 9 – x
12 = 25 – x
x = 25 – 12
x = 13
Now, 47 + x + y = 68
47 + 13 + y = 68
60 + y = 68
y = 68 – 60
y = 8
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