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Find quartile deviation {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}}

Solution:
Your problem `->` quartile deviation {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}}


ClassFrequency
`f`
`cf`
10 - 201515
20 - 302540
30 - 402060
40 - 501272
50 - 60880
---------
n = 80--


Here, `n = 80`


`Q_1` class :

Class with `(n/4)^(th)` value of the observation in `cf` column

`=(80/4)^(th)` value of the observation in `cf` column

`=(20)^(th)` value of the observation in `cf` column

and it lies in the class `20 - 30`.

`:. Q_1` class : `20 - 30`

The lower boundary point of `20 - 30` is `20`.

`:. L = 20`

`Q_1 = L + (( n)/4 - cf)/f * c`

`=20 + (20 - 15)/25 * 10`

`=20 + (5)/25 * 10`

`=20 + 2`

`=22`




`Q_3` class :

Class with `((3n)/4)^(th)` value of the observation in `cf` column

`=((3*80)/4)^(th)` value of the observation in `cf` column

`=(60)^(th)` value of the observation in `cf` column

and it lies in the class `40 - 50`.

`:. Q_3` class : `40 - 50`

The lower boundary point of `40 - 50` is `40`.

`:. L = 40`

`Q_3 = L + ((3 n)/4 - cf)/f * c`

`=40 + (60 - 60)/12 * 10`

`=40 + (0)/12 * 10`

`=40 + 0`

`=40`



Quartile deviation `=(Q_3 - Q_1)/2=(40-22)/2=18/2=9`

Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(40-22)/(40+22)=18/62=0.2903`






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