The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers.
Daily Income (in Rs) | 10 – 14 | 15 – 19 | 20 – 24 | 25 – 29 | 30 – 34 | 35 – 39 |
Number of workers | 5 | 10 | 15 | 20 | 10 | 5 |
(Hint: Compute median, lower quartile and upper quartile)
Daily Income (in Rs) Class Interval | No. of Workers (f) | Cumulative frequency (CF) |
9.5 – 14.5 | 5 | 5 |
14.5 – 19.5 | 10 | 15 |
19.5 – 24.5 | 15 | 30 |
24.5 – 29.5 | 20 | 50 |
29.5 – 34.5 | 10 | 60 |
34.5 – 39.5 | 5 | 65 |
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(a) Highest income of lowest 50% workers
32.5th item lies in the 50th cumulative frequency and the corresponding class interval is 24.5 – 29.5.
(b) Minimum income earned by top 25% workers
In order to calculate the minimum income earned by top 25% workers, we need to ascertain Q3.
48.75th item lies in 50th item and the corresponding class interval is 24.5 – 29.5.
(c) Maximum income earned by lowest 25% workers
In order to calculate the maximum income earned by lowest 25% workers, we need to ascertain Q1.
16.25th item lies in the 30th cumulative frequency and the corresponding class interval is 19.5 – 24.5