Chapter 2
Descriptive Statistics
§ 2.1
Frequency
Distributions and
Their Graphs
Frequency Histogram
A frequency histogram is a bar graph that represents
the frequency distribution of a data set.
1. The horizontal scale is quantitative and measures
the data values.
2. The vertical scale measures the frequencies of the
classes.
3. Consecutive bars must touch.
Class boundaries are the numbers that separate the
classes without forming gaps between them.
The horizontal scale of a histogram can be marked with
either the class boundaries or the midpoints.
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Class Boundaries
Example:
Find the class boundaries for the “Ages of Students” frequency
distribution.
Ages of Students
The distance from
the upper limit of
the first class to the
lower limit of the
second class is 1.
Half this
distance is 0.5.
Class
Frequency, f
Class
Boundaries
18 – 25
26 – 33
34 – 41
42 – 49
50 – 57
13
8
4
3
2
17.5  25.5
25.5  33.5
33.5  41.5
41.5  49.5
49.5  57.5
 f  30
Larson & Farber, Elementary Statistics: Picturing the World, 3e
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Frequency Histogram
Example:
Draw a frequency histogram for the “Ages of Students”
frequency distribution. Use the class boundaries.
14
Ages of Students
13
12
10
8
8
f
6
4
4
3
2
2
0
Broken axis
17.5
25.5
33.5
41.5
49.5
57.5
Age (in years)
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Frequency Polygon
A frequency polygon is a line graph that emphasizes
the continuous change in frequencies.
1. The horizontal scale is the class midpoints.
2. The vertical scale measures the frequencies of the
classes.
3. All points are connected with a straight line.
Larson & Farber, Elementary Statistics: Picturing the World, 3e
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Frequency Polygon
A frequency polygon is a line graph that emphasizes the
continuous change in frequencies.
14
Ages of Students
12
10
Line is extended
to the x-axis.
8
f
6
4
2
0
Broken axis
13.5
21.5
29.5
37.5
45.5
53.5
Age (in years)
Larson & Farber, Elementary Statistics: Picturing the World, 3e
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Midpoints
7
Relative Frequency Histogram
A relative frequency histogram has the same shape and
the same horizontal scale as the corresponding frequency
histogram.
Relative frequency
(portion of students)
0.5
0.433
Ages of Students
0.4
0.3
0.267
0.2
0.133
0.1
0.1
0.067
0
17.5
25.5
33.5
41.5
49.5
57.5
Age (in years)
Larson & Farber, Elementary Statistics: Picturing the World, 3e
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Cumulative Frequency Graph
Cumulative frequency
(portion of students)
A cumulative frequency graph or ogive, is a line graph
that displays the cumulative frequency of each class at
its upper class boundary.
30
Ages of Students
24
The graph ends
at the upper
boundary of the
last class.
18
12
6
0
17.5
25.5
33.5
41.5
49.5
57.5
Age (in years)
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Homework
Monday HW Pg 43-47 #8,19-22,25,29
Tuesday HW 7, 18, 27, 33
Larson & Farber, Elementary Statistics: Picturing the World, 3e
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Homework Pg 43-47 # 7, 18, 28, 36
7 True
18 a)44
b) 70 inches
28 and 36 see scans
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