Formula

Arrange the data in ascending order, then

Quartile `Q_i = ((i * (n+1))/4)^(th)` value of the observation, where i=1,2,3

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Examples
1. Calculate Quartile-1 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`

`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`

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2. Calculate Quartile-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`

`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`

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3. Calculate Quartile-3 from the following data
`3,13,11,15,5,4,2`

Solution:
Arranging Observations in the ascending order, We get :
`2,3,4,5,11,13,15`

Here, `n = 7`

`Q_3 = ((3(n+1))/4)^(th)` value of the observation

`=((3*8)/4)^(th)` value of the observation

`=6^(th)` value of the observation

`=13`

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4. Calculate Quartile-1 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`

`Q_1 = ((n+1)/4)^(th)` value of the observation

`=(11/4)^(th)` value of the observation

`=(2.75)^(th)` value of the observation

`=2^(nd)` observation ` + 0.75 [3^(rd) - 2^(nd)]`

`=76 + 0.75 [80 - 76]`

`=76 + 0.75 (4)`

`=76 + 3`

`=79`

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