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Home > Statistical Methods calculators > Decile deviation, Coefficient of decile deviation, Interdecile range, Semi-interdecile range for ungrouped data calculator
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Solution
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Solution provided by AtoZmath.com
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Decile deviation, Coefficient of decile deviation, Interdecile range, Semi-interdecile 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 Decile deviation, Coefficient of D.D., Interdecile range from the following data
`10,50,30,20,10,20,70,30`
Solution:
Decile deviation :
Arranging Observations in the ascending order, We get :
`10,10,20,20,30,30,50,70`
Here, `n=8`
`D_1 = ((n+1)/10)^(th)` value of the observation
`=(9/10)^(th)` value of the observation
`=(0.9)^(th)` value of the observation
`=0^(th)` observation `+0.9[1^(st)-0^(th)]`
`=0+0.9[10-0]`
`=0+0.9(10)`
`=0+9`
`=9`
`D_9 = ((9(n+1))/10)^(th)` value of the observation
`=((9*9)/10)^(th)` value of the observation
`=(8.1)^(th)` value of the observation
`=8^(th)` observation `+0.1[9^(th)-8^(th)]`
`=70+0.1[70-70]`
`=70+0.1(0)`
`=70+0`
`=70`
InterDecile range `=D_9 - D_1=70-9=61`
Decile deviation `=(D_9 - D_1)/2=(70-9)/2=61/2=30.5` (Semi-InterDecile range)
Coefficient of Decile deviation `=(D_9 - D_1)/(D_9 + D_1)=(70-9)/(70+9)=61/79=0.7722`
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