Question

The following table shows the age distribution of patients of malaria in a village during a  particular month:

Age (in years)	5 – 14	15 – 24	25 – 34	35 – 44	45 – 54	55 - 64
No. of cases	6	11	21	23	14	5

Find the average age of the patients.

Answer 1

Class	Frequency `(f_i)`	Mid values `(x_i)`	`u_i = ((x_i− A))/ ℎ = ((x_i− 29.5))/ 10`	`(f_i × u_i)`
4.5 – 14.5	6	9.5	-2	-12
14.5 – 24.5	11	19.5	-1	-11
24.5 – 34.5	21	29.5 = A	0	0
34.5 – 44.5	23	39.5	1	23
44.5 – 54.5	14	49.5	2	28
54.5 – 64.5	5	59.5	3	15
	`Ʃ f_i` = 80			`Ʃ (f_i × u_i)` = 43

Now, `A = 29.5, h = 10, Ʃ f_i = 80 and Ʃ (f_i × u_i) = 43`

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

     = `29.5 + {10 xx 43/80}`

    =29.5 + 5.375
    = 34.875
∴ 𝑥 = 34.875
∴ The average age of the patients is 34.87 years.