1. Calculate 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`

`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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2. Calculate Percentiles-70 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`

`P_70 = ((70(n+1))/100)^(th)` value of the observation

`=((70*49)/100)^(th)` value of the observation

`=(34.3)^(th)` value of the observation

`=13`

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3. Calculate 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`


`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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4. Calculate Percentiles-70 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`


`P_70` class :

Class with `((70n)/100)^(th)` value of the observation in `cf` column

`=((70*50)/100)^(th)` value of the observation in `cf` column

`=(35)^(th)` value of the observation in `cf` column

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

`:. P_70` class : `6 - 8`

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

`:. L = 6`

`P_70 = L + ((70 n)/100 - cf)/f * c`

`=6 + (35 - 34)/7 * 2`

`=6 + (1)/7 * 2`

`=6 + 0.2857`

`=6.2857`

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5. Calculate Percentiles-20 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`


`P_20` class :

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

`=((20*88)/100)^(th)` value of the observation in `cf` column

`=(17.6)^(th)` value of the observation in `cf` column

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

`:. P_20` class : `20 - 30`

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

`:. L = 20`

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

`=20 + (17.6 - 15)/25 * 10`

`=20 + (2.6)/25 * 10`

`=20 + 1.04`

`=21.04`

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5. Calculate Percentiles-70 from the following grouped data

Class	Frequency
20 - 25	110
25 - 30	170
30 - 35	80
35 - 40	45
40 - 45	40
45 - 50	35

Solution:

Class	Frequency `f`	`cf`
20 - 25	110	110
25 - 30	170	280
30 - 35	80	360
35 - 40	45	405
40 - 45	40	445
45 - 50	35	480
---	---	---
	n = 480	--

Here, `n = 480`


`P_70` class :

Class with `((70n)/100)^(th)` value of the observation in `cf` column

`=((70*480)/100)^(th)` value of the observation in `cf` column

`=(336)^(th)` value of the observation in `cf` column

and it lies in the class `30 - 35`.

`:. P_70` class : `30 - 35`

The lower boundary point of `30 - 35` is `30`.

`:. L = 30`

`P_70 = L + ((70 n)/100 - cf)/f * c`

`=30 + (336 - 280)/80 * 5`

`=30 + (56)/80 * 5`

`=30 + 3.5`

`=33.5`

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