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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