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 lowesr 25% worlers.
`{:("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):}`

Explanation

[This is an inclusive series to be converted into an exclusive series , as in the following table :

(a) M= Size of `((N)/(2))` th item
=Size of `((65)/(2))` th item
=Size of 32.5th item
32. 5th item lies in 50 cumulative frequency and the corresponding median class is 24.5-29.5. Using the formula ,
`M=(N/(2)-c.f.)/(f)xxi`
`=24.5+(65/(2)-30)/(20)xx5`
`=24.5+(32.5-30)/(20)xx5`
`=24.5+(2.5)/(20)xx5`
`=25.125`
`:.` Highest income of lowest 50% workers = Rs. 25.125.
(b) ` Q_(1)` = Size of `((N)/(4))` th item
= size of `((65)/(4))` th item
= Size of 16.25th item
16. 25th item lies in 30th cumulative frequency and the corresponding median class is 19.5-24.5.
Using the formula ,
`Q_(1)=+(N/(4)-c.f.)/(f)xxi`
`=19.5+(65/(4)-15)/(15)xx5`
`=19.5+(16.25-15)/(15)xx5`
`=19.5+(1.25)/(15)xx5`
`=19.5+0.42`
`=19.92`
Minimum income earned by the top 25% workers = Rs.19.92.
(c) `Q_(1)` = size of `3((N)/(4))` th item
= size of `3((65)/(4))` th item = Size of 48.75 th item
48. 75 th item lies in 50th cumulaive frequency and the corresponding median class is 24.5 - 29.5.
`Q_(3)=l_(1)+(3(N/(4))-c.f.)/(f)xxi`
`=24.5+(3(65/(4))-30)/(20)xx5`
`=24.5+(48.75-30)/(20)xx5`
`=24.5+(18.75)/(20)xx5=24.5+4.69`
`=29.19`
Maximum income earned by lowest 25% workers = Rs.29.19.]