Question

Find the mean age from the following frequency distribution:

Age (in years)	25 – 29	30 – 34	35 – 39	40 – 44	45 – 49	50 – 54	55 – 59
Number of persons	4	14	22	16	6	5	3

 

Answer 1

Class	Frequency `(f_i)`	Mid values `(x_i)`	`u_i = ((x_i− A))/ ℎ = ((x_i− 42))/5`	`(f_i × u_i)`
24.5 – 29.5	4	27	-3	-12
29.5 – 34.5	14	32	-2	-28
34.5 – 39.5	22	37	-1	-22
39.5 – 44.5	16	42 = A	0	0
44.5 – 49.5	6	47	1	6
49.5 – 54.5	5	52	2	10
54.5 – 59.5	3	57	3	9
	`Ʃ f_i = 70`			`Ʃ (f_i × u_i) = -37`

Now, `A = 42, h = 5, Ʃ f_i = 70 and Ʃ (f_i × u_i) = -37`

∴ Mean, 𝑥 `= A + { h xx (Ʃ (f_i × u_i))/(Ʃ f_i)}`

    = `42+{ 5xx((-37))/70}`

    =42-2.64

    =39.36

∴ 𝑥 = 39.36
∴ Mean age = 39.36 years.