1. Calculate Percentile deviation, Coefficient of P.D., Interpercentile range from the following data
`10,50,30,20,10,20,70,30`

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

Here, `n=8`

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

`=((10*9)/100)^(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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`P_90 = ((90(n+1))/100)^(th)` value of the observation

`=((90*9)/100)^(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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InterPercentile range `=P_90 - P_10=70-9=61`

Percentile deviation `=(P_90 - P_10)/2=(70-9)/2=61/2=30.5` (Semi-InterPercentile range)

Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(70-9)/(70+9)=61/79=0.7722`

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