# 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

(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

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