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_2`	70	1260-70`f_2`
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, `barx = (Σ(f_i xx x_i))/(Σf_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.`