Formula

Arrange the data in ascending order, then

Quintile `"Quintile"_i = ((i * (n+1))/5)^(th)` value of the observation, where i=1,2,3,4

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Examples
1. Calculate Quintile-4 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`

`"Quintile"_4 = ((4(n+1))/5)^(th)` value of the observation

`=((4*11)/5)^(th)` value of the observation

`=(8.8)^(th)` value of the observation

`=8^(th)` observation `+0.8[9^(th)-8^(th)]`

`=96+0.8[100-96]`

`=96+0.8(4)`

`=96+3.2`

`=99.2`

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2. Calculate Quintile-4 from the following data
`3,23,13,11,15,5,4,2`

Solution:
Arranging Observations in the ascending order, We get :
`2,3,4,5,11,13,15,23`

Here, `n=8`

`"Quintile"_4 = ((4(n+1))/5)^(th)` value of the observation

`=((4*9)/5)^(th)` value of the observation

`=(7.2)^(th)` value of the observation

`=7^(th)` observation `+0.2[8^(th)-7^(th)]`

`=15+0.2[23-15]`

`=15+0.2(8)`

`=15+1.6`

`=16.6`

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3. Calculate Quintile-2 from the following data
`4,14,12,16,6,3,1,2,3`

Solution:
Arranging Observations in the ascending order, We get :
`1,2,3,3,4,6,12,14,16`

Here, `n=9`

`"Quintile"_2 = ((2(n+1))/5)^(th)` value of the observation

`=((2*10)/5)^(th)` value of the observation

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

`=3`

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4. Calculate Quintile-3 from the following data
`73,70,71,73,68,67,69,72,76,71`

Solution:
Arranging Observations in the ascending order, We get :
`67,68,69,70,71,71,72,73,73,76`

Here, `n=10`

`"Quintile"_3 = ((3(n+1))/5)^(th)` value of the observation

`=((3*11)/5)^(th)` value of the observation

`=(6.6)^(th)` value of the observation

`=6^(th)` observation `+0.6[7^(th)-6^(th)]`

`=71+0.6[72-71]`

`=71+0.6(1)`

`=71+0.6`

`=71.6`

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