1. Calculate Decile deviation, Coefficient of D.D., Interdecile range from the following data
`10,50,30,20,10,20,70,30`

Solution:
Decile deviation :
Arranging Observations in the ascending order, We get :
`10,10,20,20,30,30,50,70`

Here, `n=8`

`D_1 = ((n+1)/10)^(th)` value of the observation

`=(9/10)^(th)` value of the observation

`=(0.9)^(th)` value of the observation

`=0^(th)` observation `+0.9[1^(st)-0^(th)]`

`=0+0.9[10-0]`

`=0+0.9(10)`

`=0+9`

`=9`

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`D_9 = ((9(n+1))/10)^(th)` value of the observation

`=((9*9)/10)^(th)` value of the observation

`=(8.1)^(th)` value of the observation

`=8^(th)` observation `+0.1[9^(th)-8^(th)]`

`=70+0.1[70-70]`

`=70+0.1(0)`

`=70+0`

`=70`

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InterDecile range `=D_9 - D_1=70-9=61`

Decile deviation `=(D_9 - D_1)/2=(70-9)/2=61/2=30.5` (Semi-InterDecile range)

Coefficient of Decile deviation `=(D_9 - D_1)/(D_9 + D_1)=(70-9)/(70+9)=61/79=0.7722`

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