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Question
Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.
| x | 10 | 30 | 50 | 70 | 90 | |
| f | 17 | f1 | 32 | f2 | 19 | Total 120 |
Solution
| x | f | fx |
| 10 | 17 | 170 |
| 30 | f1 | 30f1 |
| 50 | 32 | 1600 |
| 70 | f2 | 70f2 |
| 90 | 19 | 1710 |
| N = 120 | `sumfx=30f_1+70f_2+3480` |
Given
Mean = 50
`(sumfx)/N=50`
`(30f_1+70f_2+3480)/120=50`
30f1 + 70f2 + 3480 = 6000 ............(i)
Also,
∑f = 120
17 + f1 + 32 + f2 + 19 = 120
f1 + f2 = 52
f1 = 52 - f2
Substituting value of f1 in (i)
30(52 - f2) + 70f2 + 3480 = 6000
1560 - 30f2 + 70f2 + 3480 = 6000
40f2 + 5040 = 6000
40f2 = 6000 - 5040
40f2 = 960
`f_2 = 960/40`
f2 = 24
Hence
f1 = 52 - f2 = 52 - 24 = 28
∴ f1 = 28, f2 = 24
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