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Question
The weight of 50 workers is given below:
| Weight in Kg | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 | 100-110 | 110-120 |
| No. of Workers | 4 | 7 | 11 | 14 | 6 | 5 | 3 |
Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:
1) The upper and lower quartiles.
2) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight.
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Solution
The cumulative frequency table of the given distribution table is as follows:
| Weight in Kg | Number of workers | Cumulative frequency |
| 50-60 | 4 | 4 |
| 60-70 | 7 | 11 |
| 70-80 | 11 | 22 |
| 80-90 | 14 | 36 |
| 90-100 | 6 | 42 |
| 100-110 | 5 | 47 |
| 110-120 | 3 | 50 |
The ogive is as follows:
Number of worker = 50
1) Upper quartile (Q3) = `((3 xx 50)/4)^"th"` term = `(37.5)^th` term = 92
Lower quartile (`Q_1`) = `(50/4)^"th"` term = `(12.5)^"th"` term = 71.1
2) Through mark of 95 on the x-axis, draw a vertical line which meets the graph at point C.
Then through point C, draw a horizontal line which meets the y-axis at the mark of 39
Thus, number of workers weighing 95 kg and above = 50 - 39 = 11
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