1. Calculate Quartile-3 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`

`Q_3 = ((3(n+1))/4)^(th)` value of the observation

`=((3*26)/4)^(th)` value of the observation

`=(19.5)^(th)` value of the observation

`=3`

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2. Calculate Quartile-1 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`

`Q_1 = ((n+1)/4)^(th)` value of the observation

`=(49/4)^(th)` value of the observation

`=(12.25)^(th)` value of the observation

`=11`

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3. Calculate Quartile-3 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`


`Q_3` class :

Class with `((3n)/4)^(th)` value of the observation in `cf` column

`=((3*10)/4)^(th)` value of the observation in `cf` column

`=(7.5)^(th)` value of the observation in `cf` column

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

`:. Q_3` class : `6 - 8`

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

`:. L = 6`

`Q_3 = L + ((3 n)/4 - cf)/f * c`

`=6 + (7.5 - 7)/2 * 2`

`=6 + (0.5)/2 * 2`

`=6 + 0.5`

`=6.5`

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4. Calculate Quartile-1 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`


`Q_1` class :

Class with `(n/4)^(th)` value of the observation in `cf` column

`=(50/4)^(th)` value of the observation in `cf` column

`=(12.5)^(th)` value of the observation in `cf` column

and it lies in the class `2 - 4`.

`:. Q_1` class : `2 - 4`

The lower boundary point of `2 - 4` is `2`.

`:. L = 2`

`Q_1 = L + (( n)/4 - cf)/f * c`

`=2 + (12.5 - 5)/16 * 2`

`=2 + (7.5)/16 * 2`

`=2 + 0.9375`

`=2.9375`

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5. Calculate Quartile-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`


`Q_3` class :

Class with `((3n)/4)^(th)` value of the observation in `cf` column

`=((3*88)/4)^(th)` value of the observation in `cf` column

`=(66)^(th)` value of the observation in `cf` column

and it lies in the class `40 - 50`.

`:. Q_3` class : `40 - 50`

The lower boundary point of `40 - 50` is `40`.

`:. L = 40`

`Q_3 = L + ((3 n)/4 - cf)/f * c`

`=40 + (66 - 60)/12 * 10`

`=40 + (6)/12 * 10`

`=40 + 5`

`=45`

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6. Calculate Quartile-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`


`Q_1` class :

Class with `(n/4)^(th)` value of the observation in `cf` column

`=(480/4)^(th)` value of the observation in `cf` column

`=(120)^(th)` value of the observation in `cf` column

and it lies in the class `25 - 30`.

`:. Q_1` class : `25 - 30`

The lower boundary point of `25 - 30` is `25`.

`:. L = 25`

`Q_1 = L + (( n)/4 - cf)/f * c`

`=25 + (120 - 110)/170 * 5`

`=25 + (10)/170 * 5`

`=25 + 0.2941`

`=25.2941`

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