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`
`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`
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`
This material is intended as a summary. Use your textbook for detail explanation.
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