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Problem: quartile deviation {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} [ Calculator, Method and examples ]

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

Quartile deviation :
 Class Frequencyf cf 10 - 20 15 15 20 - 30 25 40 30 - 40 20 60 40 - 50 12 72 50 - 60 8 80 --- --- --- 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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