1. Construct an ungrouped frequency distribution table from the following data
`2,3,7,8,8,5,5,3,7,3,1,8,6,7,4,5,6,3,2,4,3,4,9,8,3`

Solution:
`2,3,7,8,8,5,5,3,7,3,1,8,6,7,4,5,6,3,2,4,3,4,9,8,3`

Here minimum value is 1 and maximum value is 9

x	Tally marks	Frequency
1
2
3
4
5
6
7
8
9
Total

For each value draw a tally mark, next to the x.
`2,3,7,8,8,5,5,3,7,3,1,8,6,7,4,5,6,3,2,4,3,4,9,8,3`

x	Tally marks	Frequency
1	|
2	||
3	||||| |
4	|||
5	|||
6	||
7	|||
8	||||
9	|
Total

Count tally marks to determine the total frequency of each x.

x	Tally marks	Frequency
1	|	1
2	||	2
3	||||| |	6
4	|||	3
5	|||	3
6	||	2
7	|||	3
8	||||	4
9	|	1
Total		`n=25`

The relative frequency

x	Frequency `f`	Relative Frequency `f/n`
1	1	`1/25=0.04=4%`
2	2	`2/25=0.08=8%`
3	6	`6/25=0.24=24%`
4	3	`3/25=0.12=12%`
5	3	`3/25=0.12=12%`
6	2	`2/25=0.08=8%`
7	3	`3/25=0.12=12%`
8	4	`4/25=0.16=16%`
9	1	`1/25=0.04=4%`
Total	`n=25`

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2. Construct an ungrouped frequency distribution table from the following data
`21,23,19,17,12,15,15,17,17,19,23,23,21,23,25,25,21,19,19,19`

Solution:
`21,23,19,17,12,15,15,17,17,19,23,23,21,23,25,25,21,19,19,19`

Here minimum value is 12 and maximum value is 25

x	Tally marks	Frequency
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Total

For each value draw a tally mark, next to the x.
`21,23,19,17,12,15,15,17,17,19,23,23,21,23,25,25,21,19,19,19`

x	Tally marks	Frequency
12	|
13
14
15	||
16
17	|||
18
19	|||||
20
21	|||
22
23	||||
24
25	||
Total

Count tally marks to determine the total frequency of each x.

x	Tally marks	Frequency
12	|	1
13		0
14		0
15	||	2
16		0
17	|||	3
18		0
19	|||||	5
20		0
21	|||	3
22		0
23	||||	4
24		0
25	||	2
Total		`n=20`

The relative frequency

x	Frequency `f`	Relative Frequency `f/n`
12	1	`1/20=0.05=5%`
13	0	`0/20=0=0%`
14	0	`0/20=0=0%`
15	2	`2/20=0.1=10%`
16	0	`0/20=0=0%`
17	3	`3/20=0.15=15%`
18	0	`0/20=0=0%`
19	5	`5/20=0.25=25%`
20	0	`0/20=0=0%`
21	3	`3/20=0.15=15%`
22	0	`0/20=0=0%`
23	4	`4/20=0.2=20%`
24	0	`0/20=0=0%`
25	2	`2/20=0.1=10%`
Total	`n=20`

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