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

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

Here, `n=10`

`P_10 = ((10(n+1))/100)^(th)` value of the observation

`=((10*11)/100)^(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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`P_90 = ((90(n+1))/100)^(th)` value of the observation

`=((90*11)/100)^(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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InterPercentile range `=P_90 - P_10=107.2-70.6=36.6`

Percentile deviation `=(P_90 - P_10)/2=(107.2-70.6)/2=36.6/2=18.3` (Semi-InterPercentile range)

Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(107.2-70.6)/(107.2+70.6)=36.6/177.8=0.2058`

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