Formula

1. Quartile `Q_i` class = `((i n)/4)^(th)` value of the observation `Q_i = L + ((i n)/4 - cf)/f * c`, where i=1,2,3

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

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

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Examples
1. Calculate Quartile-3, Deciles-7, Percentiles-20 from the following grouped data

Class	Frequency
2 - 4	3
4 - 6	4
6 - 8	2
8 - 10	1

Solution:

Class	Frequency `f`	`cf`
2 - 4	3	3
4 - 6	4	7
6 - 8	2	9
8 - 10	1	10
---	---	---
	n = 10	--

Here, `n = 10`


`Q_3` class :

Class with `((3n)/4)^(th)` value of the observation in `cf` column

`=((3*10)/4)^(th)` value of the observation in `cf` column

`=(7.5)^(th)` value of the observation in `cf` column

and it lies in the class `6 - 8`.

`:. Q_3` class : `6 - 8`

The lower boundary point of `6 - 8` is `6`.

`:. L = 6`

`Q_3 = L + ((3 n)/4 - cf)/f * c`

`=6 + (7.5 - 7)/2 * 2`

`=6 + (0.5)/2 * 2`

`=6 + 0.5`

`=6.5`

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`D_7` class :

Class with `((7n)/10)^(th)` value of the observation in `cf` column

`=((7*10)/10)^(th)` value of the observation in `cf` column

`=(7)^(th)` value of the observation in `cf` column

and it lies in the class `4 - 6`.

`:. D_7` class : `4 - 6`

The lower boundary point of `4 - 6` is `4`.

`:. L = 4`

`D_7 = L + ((7 n)/10 - cf)/f * c`

`=4 + (7 - 3)/4 * 2`

`=4 + (4)/4 * 2`

`=4 + 2`

`=6`

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`P_20` class :

Class with `((20n)/100)^(th)` value of the observation in `cf` column

`=((20*10)/100)^(th)` value of the observation in `cf` column

`=(2)^(th)` value of the observation in `cf` column

and it lies in the class `2 - 4`.

`:. P_20` class : `2 - 4`

The lower boundary point of `2 - 4` is `2`.

`:. L = 2`

`P_20 = L + ((20 n)/100 - cf)/f * c`

`=2 + (2 - 0)/3 * 2`

`=2 + (2)/3 * 2`

`=2 + 1.3333`

`=3.3333`

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2. Calculate Quartile-3, Deciles-7, Percentiles-20 from the following grouped data

X	Frequency
0	1
1	5
2	10
3	6
4	3

Solution:

`x`	Frequency `f`	`cf`
0	1	1
1	5	6
2	10	16
3	6	22
4	3	25
---	---	---
	n = 25	--

Here, `n = 25`

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

`=((3*26)/4)^(th)` value of the observation

`=(19.5)^(th)` value of the observation

`=3`

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`D_7 = ((7(n+1))/10)^(th)` value of the observation

`=((7*26)/10)^(th)` value of the observation

`=(18.2)^(th)` value of the observation

`=3`

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

`=((20*26)/100)^(th)` value of the observation

`=(5.2)^(th)` value of the observation

`=1`

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