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Question
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 |
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 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
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