3. Calculate Octile-3 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`


`"Octile"_3` class :

Class with `((3n)/8)^(th)` value of the observation in `cf` column

`=((3*10)/8)^(th)` value of the observation in `cf` column

`=(3.75)^(th)` value of the observation in `cf` column

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

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

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

`:. L=4`

`"Octile"_3=L+((3 n)/8 - cf)/f * c`

`=4+(3.75-3)/4*2`

`=4+(0.75)/4*2`

`=4+0.375`

`=4.375`

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4. Calculate Octile-6 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`


`"Octile"_6` class :

Class with `((6n)/8)^(th)` value of the observation in `cf` column

`=((6*50)/8)^(th)` value of the observation in `cf` column

`=(37.5)^(th)` value of the observation in `cf` column

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

`:. "Octile"_6` class : `6 - 8`

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

`:. L=6`

`"Octile"_6=L+((6 n)/8 - cf)/f * c`

`=6+(37.5-34)/7*2`

`=6+(3.5)/7*2`

`=6+1`

`=7`

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