The given graph represents the monthly salaries (in ₹) of workers of a factory.
Using graph answer the following:
(a) the total number of workers.
(b) the median class.
(c) the lower-quartile class.
(d) number of workers having monthly salary more than or equal to ₹6,000 but less than ₹10,000.
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| Monthly salary | cf |
|---|---|
| 0-2000 | 10 |
| 2000 - 4000 | 20 |
| 4000 - 6000 | 35 |
| 6000 - 8000 | 55 |
| 8000 - 10000 | 70 |
| 10000 - 12000 | 75 |
(a) From the graph, the cumulative frequency at ₹12,000 is 75.
Hence, the total number of workers = 75.
(b) By formula,
Median = $\frac{N + 1}{2}$
Total workers = 75
$\frac{75 + 1}{2} = \frac{76}{2} = 38$
From table,
36 to 55 worker lies in the class 6000 - 8000.
Thus, 38th worker lies in the class 6000 - 8000.
Hence, the median class = 6000 – 8000.
(c) Lower quartile = $\frac{N + 1}{4} = \frac{76}{4} = 19$
From table,
11 to 20 worker lies in the class 2000 - 4000.
Thus, 19th worker lies in the class 2000 - 4000.
Hence, the lower-quartile class = 2000 – 4000.
(d) From table,
Number of workers having salary less than ₹ 10,000 = 70
Number of workers having salary less than ₹ 6,000 = 35
Number of workers in this range = 70 − 35 = 35 workers.
Hence, the number of workers having monthly salary more than or equal to ₹ 6,000 but less than ₹ 10,000 = 35.