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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6. 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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