Question

Find the mean of the following frequency distribution is 57.6 and the total number of observation is 50.

Class	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	7	`f_1`	12	`f_2`	8	5

Answer 1

Class	Frequency `(f_i)`	Mid values`(x_i)`	`(f_i xx x_i)`
0-20	7	10	70
20-40	`f_1`	30	30`f_1`
40-60	12	50	600
60-80	18-`f_1`	70	1260-70`f_1`
80-100	8	90	720
100-120	5	110	550
Total	`sum f_i = 50`		`sum (f_i xx x_i ) = 3200-40f_1`

We have:
`7 + f_1 + 12 + f_2 + 8 + 5 = 50`
`⇒ f_1 + f_2 = 18`
`⇒ f_2 = 18 – f_1`
∴ Mean, x =`(Σ_i (f_ixx x_i))/(Σi f_i)`
⇒ 57.6 =`(3200 − 40f_1)/50`
`⇒ 40f_1 = 320`
`∴ f_1 = 8`
`And  f_2 = 18 – 8`
`⇒ f_2 = 10`
∴ The missing frequencies are` f_1 = 8 and f_2 = 10.`