1. Calculate Percentile deviation, Coefficient of P.D., Interpercentile range from the following grouped data

X	Frequency
0	1
1	5
2	10
3	6
4	3

Solution:
Percentile deviation :

`x`	Frequency `f`	`cf`
0	1	1
1	5	6
2	10	16
3	6	22
4	3	25
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	`n = 25`	--

Here, `n = 25`

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

`=((10*26)/100)^(th)` value of the observation

`=(2.6)^(th)` value of the observation

`=1`

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

`=((90*26)/100)^(th)` value of the observation

`=(23.4)^(th)` value of the observation

`=4`

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InterPercentile range `=P_90 - P_10=4-1=3`

Percentile deviation `=(P_90 - P_10)/2=(4-1)/2=3/2=1.5` (Semi-InterPercentile range)

Coefficient of Percentile deviation `=(P_90 - P_10)/(P_90 + P_10)=(4-1)/(4+1)=3/5=0.6`

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