The following is the frequency distribution of overtime (per week) performed by various workers from a certain company.
Determine the values of D_{2}, Q_{2,} and P_{61} 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 |
Solution
To draw a ogive curve, we construct a less than cumulative frequency table as given below:
Overtime (in hours) |
No. of workers |
Less than cumulative frequency |
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 D_{2}, we have to consider `(2"N")/(10)=(2xx80)/10` = 16
For Q_{2}, we have to consider `"N"/(2)=80/2` = 40
and for P_{61}, 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 D_{2}, Q_{2}, and P_{61} respectively.
∴ D_{2} ≈ 13, Q_{2} ≈ 19, P_{61} ≈ 20.5