Question

The following is the frequency distribution of overtime (per week) performed by various workers from a certain company.

Determine the values of D₂, Q_2, and P₆₁ graphically.

Overtime (in hours)	Below 8	8 – 12	12 – 16	16 – 20	20 – 24	24 and above
No. of workers	4	8	16	18	20	14

Answer 1

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

Overtime (in hours)	No. of workers (f)	Less than cumulative frequency (c.f.)
Below 8	4	4
8 – 12	8	12
12 – 16	16	28
16 – 20	18	46
20 –  24	20	66
24 and above	14	80
Total	80

Points to be plotted are (8, 4), (12, 12), (16, 28), (20, 46), (24, 66) and (28, 80)
Here, N = 80

For D₂, we have to consider `(2"N")/(10)=(2xx80)/10` = 16

For Q₂, we have to consider `"N"/(2)=80/2` = 40

and for P₆₁, we have to consider `(61"N")/(100) = (61xx80)/(100)` = 48..8
∴ We consider the values 16, 40, and 48.8 on the Y-axis. From these points, we draw the lines which are parallel to the X-axis. From the points where they intersect the less than ogive, we draw perpendiculars to X-axis. The values at the foot of perpendiculars represent the values of D₂, Q₂, and P₆₁ respectively.

∴ D₂ ≈ 13, Q₂ ≈ 19, P₆₁ ≈ 20.5