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

 

Answer 1

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`