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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