3. Calculate Quartile deviation, Coefficient of Q.D., Interquartile range from the following data
`73,70,71,73,68,67,69,72,76,71`

Solution:
Quartile deviation :
Arranging Observations in the ascending order, We get :
`67,68,69,70,71,71,72,73,73,76`

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)]`

`=68+0.75[69-68]`

`=68+0.75(1)`

`=68+0.75`

`=68.75`

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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)]`

`=73+0.25[73-73]`

`=73+0.25(0)`

`=73+0`

`=73`

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InterQuartile range `=Q_3 - Q_1=73-68.75=4.25`

Quartile deviation `=(Q_3 - Q_1)/2=(73-68.75)/2=4.25/2=2.125` (Semi-InterQuartile range)

Coefficient of Quartile deviation `=(Q_3 - Q_1)/(Q_3 + Q_1)=(73-68.75)/(73+68.75)=4.25/141.75=0.03`

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