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प्रश्न
Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.
(i) Using the table, calculate the cumulative frequency of workers.
(ii) Draw the cumulative frequency curve.
Use 2 cm = ₹500, starting the origin at ₹6,500 on X-axis, and 2 cm = 100 worker at they Y-axis.
(iii) Use your graph to write down the median wages in ₹.
| Wages in ₹ (CLass) |
No. of workers (frequency) | Cumulative frequency f(x) |
| 6500 - 7000 | 10 | - |
| 7000 - 7500 | 18 | - |
| 7500 - 8000 | 22 | - |
| 8000 - 8500 | 25 | - |
| 8500 - 9000 | 17 | - |
| 9000 - 9500 | 10 | - |
| 9500 - 10000 | 8 | - |
आलेख
योग
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उत्तर
(i)
| Wages in ₹ (CLass) |
No. of workers (frequency) | Cumulative frequency f(x) |
| 6500 - 7000 | 10 | 10 |
| 7000 - 7500 | 18 | 28 |
| 7500 - 8000 | 22 | 50 |
| 8000 - 8500 | 25 | 75 |
| 8500 - 9000 | 17 | 92 |
| 9000 - 9500 | 10 | 102 |
| 9500 - 10000 | 8 | 110 |
(ii) Plot the points (6500, 0), (7000, 10), (7500, 28), (8000, 75), (9000, 92), (9500, 102), (10000, 110) and join them by a free hand curve.
(iii) Here, N = 110
To find the median we shall construct a horizontal line at cumulative frequency
= `"N"/(2) = (110)/(2)` = 55,
intersecting the ogive at (8100, 55)
Hence, median wages = ₹8100.
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