Question

Find the mean marks per student, using assumed-mean method:

Marks	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Number of students	12	18	27	20	17	6

Answer 1

Class	Frequency `(f_i)`	Mid values `(x_i)`	Deviation `(d_i) d_i = (x_i - 25)`	`(f_i× d_i)`
0 – 10	12	5	-20	-240
10 – 20	18	15	-10	-180
20 – 30	27	25 = A	0	0
30 – 40	20	35	10	200
40 – 50	17	45	20	340
50 – 60	6	55	30	180
Total	`Ʃ f_i = 100`			`Ʃ (f_i × d_i) = 300`

Let A = 25 be the assumed mean. Then we have:

Mean, x = A + `(sum (f_i xx d_i))/(sum f_i)`

= 25+`300/100`

= 28

∴ 𝑥 = 28