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Home > Statistical Methods > Quartile deviation, Coefficient of quartile deviation, Interquartile range, Semi-interquartile range for ungrouped data calculator
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Solution
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Solution provided by AtoZmath.com
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Quartile deviation, Coefficient of quartile deviation, Interquartile range, Semi-interquartile range for ungrouped data calculator
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 1. 85,96,76,108,85,80,100,85,70,95
2. 3,13,11,11,5,4,2
3. 3,23,13,11,15,3,5,4,2
4. 69,66,67,69,64,63,65,68,72
5. 4,14,12,16,6,3,1,2,3
6. 73,70,71,73,68,67,69,72,76,71
7. 10,50,30,20,10,20,70,30
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Example1. 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`
`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`
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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