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

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

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)]`

`=67+0.1[68-67]`

`=67+0.1(1)`

`=67+0.1`

`=67.1`

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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)]`

`=73+0.9[76-73]`

`=73+0.9(3)`

`=73+2.7`

`=75.7`

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InterPercentile range `=P_90 - P_10=75.7-67.1=8.6`

Percentile deviation `=(P_90 - P_10)/2=(75.7-67.1)/2=8.6/2=4.3` (Semi-InterPercentile range)

Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(75.7-67.1)/(75.7+67.1)=8.6/142.8=0.0602`

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