3. Calculate Decile deviation, Coefficient of D.D., Interdecile range from the following data
`73,70,71,73,68,67,69,72,76,71`

Solution:
Decile deviation :
Arranging Observations in the ascending order, We get :
`67,68,69,70,71,71,72,73,73,76`

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)]`

`=67+0.1[68-67]`

`=67+0.1(1)`

`=67+0.1`

`=67.1`

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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)]`

`=73+0.9[76-73]`

`=73+0.9(3)`

`=73+2.7`

`=75.7`

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InterDecile range `=D_9 - D_1=75.7-67.1=8.6`

Decile deviation `=(D_9 - D_1)/2=(75.7-67.1)/2=8.6/2=4.3` (Semi-InterDecile range)

Coefficient of Decile deviation `=(D_9 - D_1)/(D_9 + D_1)=(75.7-67.1)/(75.7+67.1)=8.6/142.8=0.0602`

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