Arrange the data in ascending order, then

Deciles `D_i = ((i * (n+1))/10)^(th)` value of the observation, where i=1,2,3, ..., 9

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Examples
1. Calculate Deciles-3 from the following data
`10,50,30,20,10,20,70,30`

Solution:
Arranging Observations in the ascending order, We get :
`10,10,20,20,30,30,50,70`

Here, `n = 8`

`D_3 = ((3(n+1))/10)^(th)` value of the observation

`=((3*9)/10)^(th)` value of the observation

`=(2.7)^(th)` value of the observation

`=2^(nd)` observation ` + 0.7 [3^(rd) - 2^(nd)]`

`=10 + 0.7 [20 - 10]`

`=10 + 0.7 (10)`

`=10 + 7`

`=17`

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2. Calculate Deciles-7 from the following data
`10,50,30,20,10,20,70,30`

Solution:
Arranging Observations in the ascending order, We get :
`10,10,20,20,30,30,50,70`

Here, `n = 8`

`D_7 = ((7(n+1))/10)^(th)` value of the observation

`=((7*9)/10)^(th)` value of the observation

`=(6.3)^(th)` value of the observation

`=6^(th)` observation ` + 0.3 [7^(th) - 6^(th)]`

`=30 + 0.3 [50 - 30]`

`=30 + 0.3 (20)`

`=30 + 6`

`=36`

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3. Calculate Deciles-3 from the following data
`85,96,76,108,85,80,100,85,70,95`

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

Here, `n = 10`

`D_3 = ((3(n+1))/10)^(th)` value of the observation

`=((3*11)/10)^(th)` value of the observation

`=(3.3)^(th)` value of the observation

`=3^(rd)` observation ` + 0.3 [4^(th) - 3^(rd)]`

`=80 + 0.3 [85 - 80]`

`=80 + 0.3 (5)`

`=80 + 1.5`

`=81.5`

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4. Calculate Deciles-7 from the following data
`85,96,76,108,85,80,100,85,70,95`

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

Here, `n = 10`

`D_7 = ((7(n+1))/10)^(th)` value of the observation

`=((7*11)/10)^(th)` value of the observation

`=(7.7)^(th)` value of the observation

`=7^(th)` observation ` + 0.7 [8^(th) - 7^(th)]`

`=95 + 0.7 [96 - 95]`

`=95 + 0.7 (1)`

`=95 + 0.7`

`=95.7`

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