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Question
The daily wages of 80 workers in a project are given below.
| Wages (in Rs.) |
400-450 | 450-500 | 500-550 | 550-600 | 600-650 | 650-700 | 700-750 |
| No. of workers |
2 | 6 | 12 | 18 | 24 | 13 | 5 |
Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:
- the median wage of the workers.
- the lower quartile wage of workers.
- the numbers of workers who earn more than Rs. 625 daily.
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Solution
The cumulative frequency table of the given distribution is as follows:
| Wages (in Rs.) | Upper limit | No. of workers | Cumulative frequency |
| 400-450 | 450 | 2 | 2 |
| 450-500 | 500 | 6 | 8 |
| 500-550 | 550 | 12 | 20 |
| 550-600 | 600 | 18 | 38 |
| 600-650 | 650 | 24 | 62 |
| 650-700 | 700 | 13 | 75 |
| 700-750 | 750 | 5 | 80 |
The ogive is as follows:
Number of workers = n = 80
i. Median = `(n/2)^"th"` term = 40th term
Through mark 40 on the Y-axis, draw a horizontal line which meets the curve at point A.
Through point A, on the curve draw a vertical line which meets the X-axis at point B
The value of point B on the X-axis is the median, which is 605.
ii. Lower quartile (Q1) = `(80/4)^"th"` term = 20th term = 550
iii. Through mark of 625 on X-axis, draw a verticle 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 50.
Thus, the number of workers that earn more than Rs. 625 daily = 80 – 50 = 30.
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