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

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

Percentile 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

P_10 class :

Class with ((10n)/100)^(th) value of the observation in cf column

=((10*80)/100)^(th) value of the observation in cf column

=(8)^(th) value of the observation in cf column

and it lies in the class 10 - 20.

:. P_10 class : 10 - 20

The lower boundary point of 10 - 20 is 10.

:. L = 10

P_10 = L + ((10 n)/100 - cf)/f * c

=10 + (8 - 0)/15 * 10

=10 + (8)/15 * 10

=10 + 5.3333

=15.3333

P_90 class :

Class with ((90n)/100)^(th) value of the observation in cf column

=((90*80)/100)^(th) value of the observation in cf column

=(72)^(th) value of the observation in cf column

and it lies in the class 50 - 60.

:. P_90 class : 50 - 60

The lower boundary point of 50 - 60 is 50.

:. L = 50

P_90 = L + ((90 n)/100 - cf)/f * c

=50 + (72 - 72)/8 * 10

=50 + (0)/8 * 10

=50 + 0

=50

Percentile deviation =(P_90 - P_10)/2=(50-15.3333)/2=34.6667/2=17.3333

Coefficient of Percentile deviation =(P_90 - P_10)/(P_90 + P_10)=(50-15.3333)/(50+15.3333)=34.6667/65.3333=0.5306

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