4. Calculate Quartile deviation, Coefficient of Q.D., Interquartile range from the following data
`3,23,13,11,15,5,4,2`

Solution:
Quartile deviation :
Arranging Observations in the ascending order, We get :
`2,3,4,5,11,13,15,23`

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)]`

`=3+0.25[4-3]`

`=3+0.25(1)`

`=3+0.25`

`=3.25`

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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)]`

`=13+0.75[15-13]`

`=13+0.75(2)`

`=13+1.5`

`=14.5`

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InterQuartile range `=Q_3 - Q_1=14.5-3.25=11.25`

Quartile deviation `=(Q_3 - Q_1)/2=(14.5-3.25)/2=11.25/2=5.625` (Semi-InterQuartile range)

Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(14.5-3.25)/(14.5+3.25)=11.25/17.75=0.6338`

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