3. Calculate Quintile-4 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`


`"Quintile"_4` class :

Class with `((4n)/5)^(th)` value of the observation in `cf` column

`=((4*10)/5)^(th)` value of the observation in `cf` column

`=(8)^(th)` value of the observation in `cf` column

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

`:. "Quintile"_4` class : `6 - 8`

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

`:. L=6`

`"Quintile"_4=L+((4 n)/5 - cf)/f * c`

`=6+(8-7)/2*2`

`=6+(1)/2*2`

`=6+1`

`=7`

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4. Calculate Quintile-3 from the following grouped data

Class	Frequency
0 - 2	5
2 - 4	16
4 - 6	13
6 - 8	7
8 - 10	5
10 - 12	4

Solution:

Class	Frequency `f`	`cf`
0 - 2	5	5
2 - 4	16	21
4 - 6	13	34
6 - 8	7	41
8 - 10	5	46
10 - 12	4	50
---	---	---
	`n = 50`	--

Here, `n = 50`


`"Quintile"_3` class :

Class with `((3n)/5)^(th)` value of the observation in `cf` column

`=((3*50)/5)^(th)` value of the observation in `cf` column

`=(30)^(th)` value of the observation in `cf` column

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

`:. "Quintile"_3` class : `4 - 6`

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

`:. L=4`

`"Quintile"_3=L+((3 n)/5 - cf)/f * c`

`=4+(30-21)/13*2`

`=4+(9)/13*2`

`=4+1.3846`

`=5.3846`

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