2. Calculate Quartile deviation, Coefficient of Q.D., Interquartile range from the following data
`85,96,76,108,85,80,100,85,70,95`

Solution:
Quartile deviation :
Arranging Observations in the ascending order, We get :
`70,76,80,85,85,85,95,96,100,108`

Here, `n=10`

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

`=(11/4)^(th)` value of the observation

`=(2.75)^(th)` value of the observation

`=2^(nd)` observation `+0.75[3^(rd)-2^(nd)]`

`=76+0.75[80-76]`

`=76+0.75(4)`

`=76+3`

`=79`

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

`=((3*11)/4)^(th)` value of the observation

`=(8.25)^(th)` value of the observation

`=8^(th)` observation `+0.25[9^(th)-8^(th)]`

`=96+0.25[100-96]`

`=96+0.25(4)`

`=96+1`

`=97`

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InterQuartile range `=Q_3 - Q_1=97-79=18`

Quartile deviation `=(Q_3 - Q_1)/2=(97-79)/2=18/2=9` (Semi-InterQuartile range)

Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(97-79)/(97+79)=18/176=0.1023`

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