1. Calculate Quartile deviation, Coefficient of Q.D., Interquartile range from the following data
`10,50,30,20,10,20,70,30`

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

Here, `n=8`

`Q_1 = ((n+1)/4)^(th)` value of the observation

`=(9/4)^(th)` value of the observation

`=(2.25)^(th)` value of the observation

`=2^(nd)` observation `+0.25[3^(rd)-2^(nd)]`

`=10+0.25[20-10]`

`=10+0.25(10)`

`=10+2.5`

`=12.5`

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`Q_3 = ((3(n+1))/4)^(th)` value of the observation

`=((3*9)/4)^(th)` value of the observation

`=(6.75)^(th)` value of the observation

`=6^(th)` observation `+0.75[7^(th)-6^(th)]`

`=30+0.75[50-30]`

`=30+0.75(20)`

`=30+15`

`=45`

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InterQuartile range `=Q_3 - Q_1=45-12.5=32.5`

Quartile deviation `=(Q_3 - Q_1)/2=(45-12.5)/2=32.5/2=16.25` (Semi-InterQuartile range)

Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(45-12.5)/(45+12.5)=32.5/57.5=0.5652`

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