5. Calculate Deciles-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`


`D_3` class :

Class with `((3n)/10)^(th)` value of the observation in `cf` column

`=((3*88)/10)^(th)` value of the observation in `cf` column

`=(26.4)^(th)` value of the observation in `cf` column

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

`:. D_3` class : `20 - 30`

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

`:. L = 20`

`D_3 = L + ((3 n)/10 - cf)/f * c`

`=20 + (26.4 - 15)/25 * 10`

`=20 + (11.4)/25 * 10`

`=20 + 4.56`

`=24.56`

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6. Calculate Deciles-7 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`


`D_7` class :

Class with `((7n)/10)^(th)` value of the observation in `cf` column

`=((7*480)/10)^(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`.

`:. D_7` class : `30 - 35`

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

`:. L = 30`

`D_7 = L + ((7 n)/10 - cf)/f * c`

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

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

`=30 + 3.5`

`=33.5`

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