5. Calculate Octile-6 from the following grouped data

Class	Frequency
10 - 20	15
20 - 30	25
30 - 40	20
40 - 50	12
50 - 60	8
60 - 70	5
70 - 80	3

Solution:

Class	Frequency `f`	`cf`
10 - 20	15	15
20 - 30	25	40
30 - 40	20	60
40 - 50	12	72
50 - 60	8	80
60 - 70	5	85
70 - 80	3	88
---	---	---
	`n = 88`	--

Here, `n = 88`


`"Octile"_6` class :

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

`=((6*88)/8)^(th)` value of the observation in `cf` column

`=(66)^(th)` value of the observation in `cf` column

and it lies in the class `40 - 50`.

`:. "Octile"_6` class : `40 - 50`

The lower boundary point of `40-50` is `40`.

`:. L=40`

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

`=40+(66-60)/12*10`

`=40+(6)/12*10`

`=40+5`

`=45`

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6. Calculate Octile-3 from the following grouped data

Class	Frequency
10 - 20	15
20 - 30	25
30 - 40	20
40 - 50	12
50 - 60	8
60 - 70	5
70 - 80	3

Solution:

Class	Frequency `f`	`cf`
10 - 20	15	15
20 - 30	25	40
30 - 40	20	60
40 - 50	12	72
50 - 60	8	80
60 - 70	5	85
70 - 80	3	88
---	---	---
	`n = 88`	--

Here, `n = 88`


`"Octile"_3` class :

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

`=((3*88)/8)^(th)` value of the observation in `cf` column

`=(33)^(th)` value of the observation in `cf` column

and it lies in the class `20 - 30`.

`:. "Octile"_3` class : `20 - 30`

The lower boundary point of `20-30` is `20`.

`:. L=20`

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

`=20+(33-15)/25*10`

`=20+(18)/25*10`

`=20+7.2`

`=27.2`

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