Formula

Arrange the data in ascending order, then

Octile `"Octile"_i = ((i * (n+1))/8)^(th)` value of the observation, where i=1,2,3,...,7

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Examples
1. Calculate Octile-5 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`

`"Octile"_5 = ((5(n+1))/8)^(th)` value of the observation

`=((5*11)/8)^(th)` value of the observation

`=(6.875)^(th)` value of the observation

`=6^(th)` observation `+0.875[7^(th)-6^(th)]`

`=85+0.875[95-85]`

`=85+0.875(10)`

`=85+8.75`

`=93.75`

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2. Calculate Octile-2 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`

`"Octile"_2 = ((2(n+1))/8)^(th)` value of the observation

`=((2*9)/8)^(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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3. Calculate Octile-5 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`

`"Octile"_5 = ((5(n+1))/8)^(th)` value of the observation

`=((5*11)/8)^(th)` value of the observation

`=(6.875)^(th)` value of the observation

`=6^(th)` observation `+0.875[7^(th)-6^(th)]`

`=85+0.875[95-85]`

`=85+0.875(10)`

`=85+8.75`

`=93.75`

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4. Calculate Octile-5 from the following data
`69,66,67,69,64,63,65,68,72`

Solution:
Arranging Observations in the ascending order, We get :
`63,64,65,66,67,68,69,69,72`

Here, `n=9`

`"Octile"_5 = ((5(n+1))/8)^(th)` value of the observation

`=((5*10)/8)^(th)` value of the observation

`=(6.25)^(th)` value of the observation

`=6^(th)` observation `+0.25[7^(th)-6^(th)]`

`=68+0.25[69-68]`

`=68+0.25(1)`

`=68+0.25`

`=68.25`

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