1. Calculate Quartile deviation 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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Inter Quartile 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`

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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2. Calculate Quartile deviation 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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Inter Quartile range `=Q_3 - Q_1=97-79=18`

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

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

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3. Calculate Quartile deviation 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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Inter Quartile 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`

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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