2. Calculate Decile deviation, Coefficient of D.D., Interdecile range from the following data
`85,96,76,108,85,80,100,85,70,95`

Solution:
Decile deviation :
Arranging Observations in the ascending order, We get :
`70,76,80,85,85,85,95,96,100,108`

Here, `n=10`

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

`=(11/10)^(th)` value of the observation

`=(1.1)^(th)` value of the observation

`=1^(st)` observation `+0.1[2^(nd)-1^(st)]`

`=70+0.1[76-70]`

`=70+0.1(6)`

`=70+0.6`

`=70.6`

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

`=((9*11)/10)^(th)` value of the observation

`=(9.9)^(th)` value of the observation

`=9^(th)` observation `+0.9[10^(th)-9^(th)]`

`=100+0.9[108-100]`

`=100+0.9(8)`

`=100+7.2`

`=107.2`

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InterDecile range `=D_9 - D_1=107.2-70.6=36.6`

Decile deviation `=(D_9 - D_1)/2=(107.2-70.6)/2=36.6/2=18.3` (Semi-InterDecile range)

Coefficient of Decile deviation `=(D_9 - D_1)/(D_9 + D_1)=(107.2-70.6)/(107.2+70.6)=36.6/177.8=0.2058`

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