1. Calculate Octile-5 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`

`"Octile"_5 = ((5(n+1))/8)^(th)` value of the observation

`=((5*26)/8)^(th)` value of the observation

`=(16.25)^(th)` value of the observation

`=3`

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2. Calculate Octile-3 from the following grouped data

X	Frequency
10	3
11	12
12	18
13	12
14	3

Solution:

`x`	Frequency `f`	`cf`
10	3	3
11	12	15
12	18	33
13	12	45
14	3	48
---	---	---
	`n = 48`	--

Here, `n = 48`

`"Octile"_3 = ((3(n+1))/8)^(th)` value of the observation

`=((3*49)/8)^(th)` value of the observation

`=(18.375)^(th)` value of the observation

`=12`

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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`

---

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`

---

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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