Formula

Arrange the data in ascending order, then 1. Quartile `Q_i = ((i * (n+1))/4)^(th)` value of the observation, where i=1,2,3

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

3. 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 Quartile-1, Deciles-3, Percentiles-20 from the following data
3,13,11,11,5,4,2

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

Here, `n = 7`

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

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

`=2^(nd)` value of the observation

`=3`

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

`=(3(8/10))^(th)` value of the observation

`=(2.4)^(th)` value of the observation

`=2^(nd)` observation ` + 0.4 [3^(rd) - 2^(nd)]`

`=3 + 0.4 [4 - 3]`

`=3 + 0.4 (1)`

`=3 + 0.4`

`=3.4`

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

`=(20(8/100))^(th)` value of the observation

`=(1.6)^(th)` value of the observation

`=1^(st)` observation ` + 0.6 [2^(nd) - 1^(st)]`

`=2 + 0.6 [3 - 2]`

`=2 + 0.6 (1)`

`=2 + 0.6`

`=2.6`

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2. Calculate Quartile-2, Deciles-6, Percentiles-45 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_2 = ((2(n+1))/4)^(th)` value of the observation

`=(2(11/4))^(th)` value of the observation

`=(5.5)^(th)` value of the observation

`=5^(th)` observation ` + 0.5 [6^(th) - 5^(th)]`

`=85 + 0.5 [85 - 85]`

`=85 + 0.5 (0)`

`=85 + 0`

`=85`

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`D_6 = ((6(n+1))/10)^(th)` value of the observation

`=(6(11/10))^(th)` value of the observation

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

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

`=85 + 0.6 [95 - 85]`

`=85 + 0.6 (10)`

`=85 + 6`

`=91`

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`P_45 = ((45(n+1))/100)^(th)` value of the observation

`=(45(11/100))^(th)` value of the observation

`=(4.95)^(th)` value of the observation

`=4^(th)` observation ` + 0.95 [5^(th) - 4^(th)]`

`=85 + 0.95 [85 - 85]`

`=85 + 0.95 (0)`

`=85 + 0`

`=85`

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