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

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

Decile 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

D_1 class :

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

=(80/10)^(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.

:. D_1 class : 10 - 20

The lower boundary point of 10 - 20 is 10.

:. L = 10

D_1 = L + (( n)/10 - cf)/f * c

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

=10 + (8)/15 * 10

=10 + 5.3333

=15.3333

D_9 class :

Class with ((9n)/10)^(th) value of the observation in cf column

=((9*80)/10)^(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.

:. D_9 class : 50 - 60

The lower boundary point of 50 - 60 is 50.

:. L = 50

D_9 = L + ((9 n)/10 - cf)/f * c

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

=50 + (0)/8 * 10

=50 + 0

=50

Decile deviation =(D_9 - D_1)/2=(50-15.3333)/2=34.6667/2=17.3333

Coefficient of Decile deviation =(D_9 - D_1)/(D_9 + D_1)=(50-15.3333)/(50+15.3333)=34.6667/65.3333=0.5306

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