Arrange the data in ascending order, then

Percentiles `P_i = ((i * (n+1))/100)^(th)` value of the observation, where i=1,2,3, ..., 99

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Examples
1. Calculate Percentiles-20 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`

`P_20 = ((20(n+1))/100)^(th)` value of the observation

`=((20*9)/100)^(th)` value of the observation

`=(1.8)^(th)` value of the observation

`=1^(st)` observation ` + 0.8 [2^(nd) - 1^(st)]`

`=10 + 0.8 [10 - 10]`

`=10 + 0.8 (0)`

`=10 + 0`

`=10`

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2. Calculate Percentiles-75 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`

`P_75 = ((75(n+1))/100)^(th)` value of the observation

`=((75*9)/100)^(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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3. Calculate Percentiles-20 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`

`P_20 = ((20(n+1))/100)^(th)` value of the observation

`=((20*11)/100)^(th)` value of the observation

`=(2.2)^(th)` value of the observation

`=2^(nd)` observation ` + 0.2 [3^(rd) - 2^(nd)]`

`=76 + 0.2 [80 - 76]`

`=76 + 0.2 (4)`

`=76 + 0.8`

`=76.8`

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4. Calculate Percentiles-75 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`

`P_75 = ((75(n+1))/100)^(th)` value of the observation

`=((75*11)/100)^(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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