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Question
Find the missing frequencies in the following frequency distribution if its 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=3480 + 30f_1 +70f_2` |
It is give that
Mean = 50
⇒ `(sumfx)/N = 50`
⇒ `(3480+30f_1 + 70f_2)/N = 50 `
⇒ `3480 + 30f_1 + 70f_2 = 50 (120)`
⇒`30f_1 + 70f_2 = 6000 - 3480`
⇒ `10 (3f_1 +7f_2) = 10(252)`
⇒`3f_1 + 7f_2 = 252 .......... (1)`[∵ Divide by 10]
And N = 120
⇒`17 +f_1+ 32 + f_2 + 19 = 120`
⇒ `68 + f_1 + f_2 = 120`
⇒ `f_1 + f_2 = 120 -68`
⇒ `f_1 + f_2 = 52`
Multiply with '3' on both sides
⇒ `3f_1 + 3f_2 = 156 ...... (2)`
Substarcting equation (2) frm equation (1)
`3 f_1 + 7 f_2 - 3 f_1 - 3 f_2 = 252 -156`
⇒ `4 f_2 = 96`
⇒ `f_2 = 96 / 4`
⇒`f_2 = 24`
Put value of f2 in equation (1)
⇒`3f_1 + 7 xx 24 = 250`
⇒ `3f_1 = 252 - 168 - 84`
⇒ `f_1= 84/3 = 28`
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