QQuestion
The given graph represents the monthly salaries, in rupees, of workers of a factory.
Using the graph, find:
(a) the total number of workers.
(b) the median class.
(c) the lower-quartile class.
(d) the number of workers with monthly salary greater than or equal to ₹6,000 but less than ₹10,000.
✓Answer
From the graph, the cumulative frequencies are:
| Monthly salary (₹) | Cumulative frequency |
|---|---|
| 0–2,000 | 10 |
| 2,000–4,000 | 20 |
| 4,000–6,000 | 35 |
| 6,000–8,000 | 55 |
| 8,000–10,000 | 70 |
| 10,000–12,000 | 75 |
(a) The cumulative frequency at ₹12,000 is 75.
Therefore, the total number of workers is 75.
(b) Median position = \frac{\mathrm{N}+1}{2}
= \frac{75+1}{2} = 38th observation
The 38th observation lies in the class ₹6,000–₹8,000.
Therefore, the median class is ₹6,000–₹8,000.
(c) Lower-quartile position = \frac{\mathrm{N}+1}{4}
= \frac{75+1}{4} = 19th observation
The 19th observation lies in the class ₹2,000–₹4,000.
Therefore, the lower-quartile class is ₹2,000–₹4,000.
(d) Number of workers with salary less than ₹10,000 = 70
Number of workers with salary less than ₹6,000 = 35
Required number of workers = 70 − 35 = 35
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