Question

The following table shows the age distribution of head of the families in a certain country. Determine the third, fifth and eighth decile of the distribution graphically.

Age of head of family (in years)	Numbers (million)
Under 35	46
35 – 45	85
45 – 55	64
55 – 65	75
65 – 75	90
75 and Above	40

Answer 1

To draw a ogive curve, we construct a less than cumulative frequency table as given below:

Age of head of family (in years)	Numbers (million) (f)	Less than cumulative frequency (c.f.)
Under 35	46	46
35 – 45	85	131
45 – 55	64	195
55 – 65	75	270
65 – 75	90	360
75 and Above	40	400
Total	400

Points to be plotted are (35, 46), (45, 131), (55, 195), (65, 270), (75, 360), (85, 400).

N = 400
For D₃, we have to consider `(3"N")/(10)=(3(400))/(10)` = 120,

For D₅, we have to consider `(5"N")/(10)=(5(400))/(10)` = 200

For D₈, we have to consider `(8"N")/(10)=(8(400))/(10)` = 320
∴ We consider the values 120, 200, and 320 on Y-axis. From these points, we draw the lines parallel to X-axis. From the points where they intersect the less than ogive, we draw perpendiculars on the X-axis. The foot of the perpendicular represents the values of D₃, D_5, and D₈.

∴ D₃ ≈ 44, D₅ ≈ 55.5, and D₈ ≈ 70