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The following is the frequency distribution of overtime (per week) performed by various workers from a certain company. Determine the values of D2, Q2, and P61 graphically. - Mathematics and Statistics

Graph
Sum

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

Determine the values of D2, Q2, 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
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Solution

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

Concept: Graphical Location of Partition Values
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