

Presentation of raw or listed data into table form
showing the variable and its frequencies. (Fancy
word for a table!)
3 types
1. Categorical
2. Ungrouped
3. Grouped
For quantitative variables
Rating of a Sociology Professor
Rating
Frequency
Superior
6
Good
28
Average
25
Poor
12
Inferior
3
Farm Population of the U.S. from 1940 to 1990
Year
Farm Population in
millions
1940
30.5
1950
23
1960
15.6
1970
9.7
1980
7.9
1990
7.3
Tread Depth of Tires
Tread Depth
Frequency
0–3
4
4–7
15
8 – 11
25
12 – 15
5
16 – 19
3
Tread Depth
Frequency
0–3
4
4–7
15
8 – 11
25
12 – 15
5
16 – 19
3
*Boundaries show the continuous nature
of the distribution.

Each of the following represents one class in
a grouped frequency distribution. Find the
boundaries for each class.
◦ A) 20 – 29
◦ B) 300 – 399
◦ C) 5.5 – 6.5
◦ D) 67.2 – 68.2
Tread Depth
Frequency
0–3
4
4–7
15
8 – 11
25
12 – 15
5
16 – 19
3
To find the width of a class, subtract any
two consecutive lower class limits.
Tread Depth
Frequency
0–3
4
4–7
15
8 – 11
25
12 – 15
5
16 – 19
3
To find the midpoint of a class,
average the upper and lower limits of that class.
1)
Generally use between 5 and 20 classes.
2)
Classes must be mutually exclusive.
3)
Classes must be continuous.
4)
Classes must be exhaustive.
5)
Classes must be the same width. (exception:
open-ended distribution)
Age
Time
0-9
Below 100
10 - 19
101 - 110
20 - 29
111 - 120
30 - 39
121 - 130
40 - 49
131 - 140
50 and older
141 - 140
85
81
65
58
47
30
51
47
92
85
42
55
37
31
82
35
63
33
44
93
77
57
44
74
63
67
46
73
52
53
1.
2.
3.
4.
5.
Find the range (Difference between the
highest and lowest data value)
Find an appropriate class width by using the
following formula: w = R/# of classes
(round up the value to the next whole #)
Select an appropriate starting point. (lowest
value is usually sufficient) Then add the
class width to get each consecutive class
lower limit.
Subtract 1 from 2nd lower limit to get 1st
upper class limit and then add width.
Tally data.
Proportion of each frequency out of the total (n).
Can be expressed as a decimal or a percent
Tread Depth of Tires
Tread Depth
Frequency (f)
Relative
Frequency (rf)
0–3
4
4/52=.077 or 7.7%
4–7
15
15/52=.288 or 28.8%
8 – 11
25
25/52=.481or 48.1%
12 – 15
5
5/52=.096 or 9.6%
16 – 19
3
3/52=.058 or 5.8%
n = 52
you don’t
need to show
all 3 values .
decimal or % is
fine
The sum of the frequencies accumulated
up to that class.
Tread Depth of Tires
Tread Depth
Frequency
Cumulative
Frequency
0–3
4
4
4–7
15
4+ 15 = 19
8 – 11
25
19 + 25 = 44
12 – 15
5
44 + 5 = 49
16 – 19
3
49 + 3 = 52
only show the
final number
in each row
The sum of the relative frequencies
up to that class or the proportion of each
cumulative frequency (last row should always be 100%)
Tread Depth of Tires
Tread
Depth
Frequency
rf
rcf
0–3
4
7.7%
4–7
15
28.8%
7.7 + 28.8 = 36.5%
8 – 11
25
48.1%
36.5 + 48.1 = 84.6%
12 – 15
5
9.6%
84.6 + 9.6 = 94.2%
16 – 19
3
5.8%
94.2 + 5.8 = 100%
7.7%
Tread
Depth
Frequency
0–3
4
4–7
15
8 – 11
25
12 – 15
5
16 – 19
3