Organizing & Graphing
“Quantitative” Data Sets
Frequency Distribution
Histogram
Frequency Polygon
Ogive
Data Set
90 59 75 81
66 95 75 71
106 78 81 68
84 70 109 112
105 47 89 62
83 95 58 91
104 100 59
82 69 72
97 44 74
97 80 75
Frequency Distribution
• Step #1: Count the Data Set: n = 36
• Divide the data set up into groups
using the rule: 2k > n. Example: 21=2,
22=4, 23=8, 24=16, 25=32, 26=64.
• Notice, 25=32 is less than 36, but
26=64 is greater 36, so the number of
groups you need is k = 6
Step # 2
Find the largest (Xmax) and the
smallest (Xmin) numbers in the
data set.
Xmax & Xmin
90 59 75 81
66 95 75 71
106 78 81 68
84 70 109 112
105 47 89 62
83 95 58 91
104 100 59
82 69 72
97 44 74
97 80 75
Step # 3
• Calculate the Range of the Data Set
• Range = Xmax – Xmin
• Range = 112 – 44
• Range = 68
Step # 4
• Calculate the Width of each Group
• Width = Range/# of Groups
• Width = 68/6
• Width = 11.33
• Round your answer to 12
Now we need to establish a set of rules to use
for organizing the data set.
The idea is to put each data element in one of
the categories we have established.
The procedure is to use Xmin and the Width.
“The Rules”
Boundaries
Group Begin End Tally
I to
II to
III to
IV to
V to
VI to
Frequency Distribution
Boundaries
Group Begin End Tally
I 44 to 55
II 56 to 67
III 68 to 79
IV 80 to 91
V 92 to 103
VI 104 to 115
Boundaries
90 59 75 81
Group Begin End Tally
66 95 75 71
106 78 81 68 I 44 to 55
84 70 109 112 II 56 to 67
105 47 89 62
83 95 58 91 III 68 to 79
104 100 59 IV 80 to 91
82 69 72
V 92 to 103
97 44 74
97 80 75 VI 104 to 115
Frequency Distribution
Boundaries
Group Begin End Frequency
I 44 to 55 2
II 56 to 67 5
III 68 to 79 10
IV 80 to 91 9
V 92 to 103 5
VI 104 to 115 5
Histogram
12
10
8
6
4
2
0
. I II III IV V VI .
Frequency Polygon
12
10
8
6
4
2
0
. I II III IV V VI .
Ogive
40
35
30
25
20
15
10
5
0
. I II III IV V VI
Making things Relative
Divide all the frequencies by the
size of the data set.
Relative Frequency
Distribution
Relative
Group Bounds Frequency
I 44-55 2/36
II 56-67 5/36
III 68-79 10/36
IV 80-91 9/36
V 92-103 5/36
VI 104-115 5/36
Relative Histogram
0.3
0.25
0.2
0.15
0.1
0.05
0
. I II III IV V VI .
Relative Frequency Polygon
0.3
0.25
0.2
0.15
0.1
0.05
0
. I II III IV V VI .
Relative Ogive
1.2
1
0.8
0.6
0.4
0.2
0
. I II III IV V VI
Microsoft Excel
Chart Construction
Demonstration