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Question
The mean of the following frequency distribution is 25.8 and the sum of all the frequencies is 50. Find x and y.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 7 | x | 15 | y | 10 |
Solution
| Class Interval | xi | fi | fixi |
| 0-10 | 5 | 7 | 35 |
| 10-20 | 15 | x | 15x |
| 20-30 | 25 | 15 | 375 |
| 30-40 | 35 | y | 35y |
| 40-50 | 45 | 10 | 450 |
| Total | 50 | 860 + 15x + 35y |
`Σf_i = x_1 + x_2 + ..... + x_n`
50 = 7 + x + 15 + y + 10
⇒ x + y + 32 = 50
⇒ x + y = 18 ........... (i)
`barx = (Σf_ix_i)/(Σf)`
`25.8 = (860 + 15x + 35y )/50`
⇒ 15x + 35y + 860 = 1290
⇒ 15x + 35y = 430
⇒ 3x + 7y = 86 ............. (ii)
Multiplying (i) by 3 and subtracting from (ii)
4y = 32
⇒ y = 8
Putting value of y in (i)
x + 8 = 18
x = 10
Therefore, x = 10 and y = 8
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