Question

Find mean and mode of the following distribution:

Class	Frequency
0-10	3
10-20	6
20-30	11
30-40	10
40-50	13
50-60	3
60-70	4

Answer 1

Class	Frequency (fi)	Class mark (xi)	fixi
0-10	3	5	15
10-20	6	15	90
20-30	11	25	275
30-40	10	35	350
40-50	13	45	585
50-60	3	55	165
60-70	4	65	260
Total	`sum f_i = 50`		`sum f_i x_i = 1740`

`sum f_i = 3 + 6 + 11 + 10 + 13 + 3 + 4`

= 50

`sum f_ix_i = 15 + 90 + 275 + 350 + 585 + 165 + 260`

= 1740

Mean = `(sum f_ix_i)/(sum f_i)`

= `1740/50`

= 34.8

Highest frequency (h) = 10

Modal class = 40-50

∴ l = 40, h = 10, f₁ = 13, f₀ = 10 and f₂ = 3

Mode = `l + (f_1 - f_0)/(2f_1 - f_0 - f_2) xx h`

= `40 + (13 - 10)/(2(13) - 10 - 3) xx 10`

= `40 + (13 - 10)/(26 - 13) xx 10`

= `40 + (3)/(13) xx 10`

= `40 + 30/13`

= 40 + 2.31

= 42.31