5. Calculate Quintile-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`


`"Quintile"_3` class :

Class with `((3n)/5)^(th)` value of the observation in `cf` column

`=((3*88)/5)^(th)` value of the observation in `cf` column

`=(52.8)^(th)` value of the observation in `cf` column

and it lies in the class `30 - 40`.

`:. "Quintile"_3` class : `30 - 40`

The lower boundary point of `30-40` is `30`.

`:. L=30`

`"Quintile"_3=L+((3 n)/5 - cf)/f * c`

`=30+(52.8-40)/20*10`

`=30+(12.8)/20*10`

`=30+6.4`

`=36.4`

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6. Calculate Quintile-1 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`


`"Quintile"_1` class :

Class with `(n/5)^(th)` value of the observation in `cf` column

`=(480/5)^(th)` value of the observation in `cf` column

`=(96)^(th)` value of the observation in `cf` column

and it lies in the class `20 - 25`.

`:. "Quintile"_1` class : `20 - 25`

The lower boundary point of `20-25` is `20`.

`:. L=20`

`"Quintile"_1=L+(( n)/5 - cf)/f * c`

`=20+(96-0)/110*5`

`=20+(96)/110*5`

`=20+4.3636`

`=24.3636`

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