Question

Find the mean of the following data, using the assumed-mean method:

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100	100 – 120
Frequency	20	35	52	44	38	31

Answer 1

Class	Frequency `(f_i)`	Mid values `(x_i)`	Deviation `(d_i) d_i = (x_i – 50)`	`(f_i  × d_i)`
0 – 20	20	10	-40	-800
20 – 40	35	30	-20	-700
40 – 60	52	50 = A	0	0
60 – 80	44	70	20	880
80 – 100	38	90	40	1520
100 – 120	31	110	60	1860
	`Ʃ f_i` = 220			`Ʃ (f_i × d_i)` = 2760

Let A = 50 be the assumed mean. Then we have:

Mean, x = A +`(Ʃ (f_i × d_i))/( Ʃ f_i)`

              = 50 + `2760/220`

             = 50+ 12.55

∴ x = 62.55