Frequency Distributions and their Graphs

1
Lesson 2.2 Frequency Distributions and their
Graphs
You will learn to Create a frequency
distribution Create graphs to display data
2
A frequency distribution is a table that shows
classes or intervals of data entries with a count
of the number of entries in each class.
The frequency ( f ) of a class is the number of
data entries in that class.
3
Example of a Frequency Distribution for the
length of phone calls
Class Frequency f
0 lt x lt 5 5
5 lt x lt 10 8
10 lt x lt 15 6
15 lt x lt 20 8
20 lt x lt 25 5
25 lt x lt 30 4
Number of minutes
Number of calls
Lower Limits
Upper Limits
4
The class width is the distance between the
lower limits or the upper limits.
Class Frequency f
0 lt x lt 5 5
5 lt x lt 10 8
10 lt x lt 15 6
15 lt x lt 20 8
20 lt x lt 25 5
25 lt x lt 30 4
5
5
Constructing a Frequency Distribution

Step 1 How many classes will you have?
The number of classes should always be between 5
and 20.
6
Step 2 find the class width
class width range ? of classes
Always go UP to the next integer
4.9
5
34 ? 7 ____, width is _____
72 ? 9 ____, width is _____
8
9
46 ? 5 ____, width is _____
9.2
10
7
Constructing a Frequency Distribution

Step 3 find class limits
Use the lowest data entry as the lower limit of
the first class.
Find the remaining lower limits by adding the
class width to the previous limit.
8
Constructing a Frequency Distribution

(if the data has been sorted, tallying is
unnecessary)
9
Create a Frequency Distribution Table for the
of minutes 30 people spent on the internet. (use
6 classes)
50 40 41 17 11 7 22 44 28 21 19 23
37 51 54 42 88 41 78 56 72 56 17 7
70 30 80 56 29 33
range
88
7
81
width
13.5?
14
81 ?
6
10
Number of Minutes on the Internet
Class Tally f
7 lt x lt 21
21 lt x lt 35
35 lt x lt 49
49 lt x lt 63
63 lt x lt 77
77 lt x lt 91
of classes
6
Class width
14
Lowest entry?
Lower Limits?
Upper Limits?
11
Number of Minutes on the Internet
50 40 41 17 11 7 22 44 28 21 19 23
37 51 54 42 88 41 78 56 72 56 17 7
70 30 80 56 29 33
12
Number of Minutes on the Internet
Class Tally f
7 lt x lt 21 6
21 lt x lt 35 7
35 lt x lt 49 6
49 lt x lt 63 6
63 lt x lt 77 2
77 lt x lt 91 3
? f
30
? means sum of
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Practice Time!! 2.2.A
14
The class midpoint is the numerical value that is
exactly in the middle of each class.
midpoint
15
Number of Minutes on the Internet
Class Midpoint f
7 lt x lt 21 14 8
21 lt x lt 35 28 12
35 lt x lt 49 42 12
49 lt x lt 63 56 10
63 lt x lt 77 70 4
77 lt x lt 91 84 4
16
A Frequency Histogram is a bar graph that
represents the frequency distribution of a data
set.
title ? identifies the study
horizontal scale ? use the midpoints or class
boundaries
vertical scale ? use the frequencies Choose your
own scale.
Consecutive bars must touch
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Internet Usage of 50 people (labeled with
midpoints)
14
12
12
12
10
10
8
frequency (number of subscribers)
8
4
6
4
4
2
14 28 42 56 70 84
time online (in minutes)
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Internet Usage of 50 People (labeled with class
boundaries)









14
12
12
12
10
10
8
frequency (number of subscribers)
8
4
6
4
4
2
7 21 35 49 63 77 91
time online (in minutes)
19
A frequency polygon is a line graph that shows
the continuous change in frequencies.
horizontal scale ? use the midpoints
vertical scale ? use the frequencies Choose your
own scale.
20
Internet Usage
the graph creates a polygon with the horizontal
axis









14
12
10
frequency (number of subscribers)
8
6
4
2
12.5 24.5 36.5 48.5 60.5 72.5 84.5
time online in minutes
21
Lets Practice!! 2.2.B
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The relative frequency of a class is the
percent of the data in that class.
relative frequency
relative frequency
1
23
Number of Minutes on the Internet
Class Midpoint f Relative Frequency
7 lt x lt 21 14 8
21 lt x lt 35 28 12
35 lt x lt 49 42 12
49 lt x lt 63 56 10
63 lt x lt 77 70 4
77 lt x lt 91 84 4
.16
.24
.24
.20
.08
.08
? f 50
? f /n 1
24
A relative frequency graph is a bar graph that
displays percentage of each class to the whole.
title ? identifies the study
horizontal scale ? midpoints or
class boundaries
vertical scale ? use the relative frequencies as
percentages Choose your own scale.
Consecutive bars must touch
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Internet Usage of 50 People









Relative frequency (percent of subscribers)
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Its Practice Time!! 2.2.C
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The cumulative frequency of a class is the sum
of the frequencies for that class and all
previous classes.
The cumulative frequency of the last class is
always equal to the sample size.
28
Number of Minutes on the Internet
Class Midpoint f Cumulative Frequency
7 lt x lt 21 14 8
21 lt x lt 35 28 12
35 lt x lt 49 42 12
49 lt x lt 63 56 10
63 lt x lt 77 70 4
77 lt x lt 91 84 4
8
8 12
20
20 12
32
32 10
42
42 4
46
46 4
50
? f
50
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Number of Minutes on the Internet
Class f Cumulative Frequency Cumulative Relative Frequency
7 lt x lt 21 8
21 lt x lt 35 12
35 lt x lt 49 12
49 lt x lt 63 10
63 lt x lt 77 4
77 lt x lt 91 4
8
.16
8/50
8 12
20
.40
20/50
20 12
32
.64
32/50
32 10
.84
42/50
42
42 4
.92
46/50
46
46 4
1.00
50/50
50
? f
50
30
A cumulative frequency graph or Ogive, is a line
graph that displays the cumulative frequency of
each class at its upper class boundary.
horizontal scale ? class boundaries
vertical scale ? cumulative frequencies Choose
your own scale
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Internet Usage of 50 people







Always begin at zero.
7 21 35 49 63 77 91
time online in minutes
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Practice Time!! 2.2.D
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Review Practice Time!!
34
Lesson 2.1 Graphing Data
You will learn to display data in a circle
graph and a Pareto Graph organize data in a
stem-and-leaf plot and a dot plot display data
in a time series graph
35
Circle Graphs and Bar Graphs are used to
display qualitative data.
36
A circle graph shows relationships of parts to a
whole.
It is easy to compare the size of each part to
the whole.
37
Convert the frequency of each class into a
percent.
then multiply by 100
Percents are used to label circle graphs.
38
Convert the frequency of each class into a degree.
angle percent 360
Degrees are used to create circle graphs.
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Cellular Phones
Type f Rel Freq. Angle
T-Mobile 3
Sprint 1
Cingular 6
Nextel 30
Verizon 20

18
.05
5
.02
2
6
36
.10
10
.50
180
50
120
.33
33
360
100
n 60
40
Cellular Phones
41
A Bar Graph displaying qualitative data should be
drawn with space between bars of equal width.
It is easy to compare the sizes of the parts to
each other.
42
Cellular Phones
Type f Rel Freq. Angle
T-Mobile 3
Sprint 1
Cingular 6
Nextel 30
Verizon 20

18
.05
5
.02
2
6
36
.10
10
.50
180
50
120
.33
33
360
100
n 60
43
Cellular Phones
35 30 25 20 15 10 5







Number of Phones
Sprint
Nextel
Verizon
Cingular
T-Mobile
Type of Service
44
Cellular Phones
Type f Rel Freq. Angle
T-Mobile 3
Sprint 1
Cingular 6
Nextel 30
Verizon 20

18
.05
5
.02
2
6
36
.10
10
.50
180
50
120
.33
33
360
100
n 60
45
Cellular Phones
.70 .60 .50 .40 .30 .20 .10







Relative Frequency
Sprint
Nextel
Verizon
Cingular
T-Mobile
Type of Service
46
A Pareto chart is a bar graph
Bars in a Pareto chart are always arranged in
descending order
47
Cellular Phones
35 30 25 20 15 10 5







Number of Phones
Sprint
Nextel
Verizon
Cingular
T-Mobile
Type of Service
48
Practice A 2.1.A
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We display quantitative data to identify a
pattern of variability.
One of the simplest graphs used is the dot plot.
50
In a dot plot each data entry is plotted (using a
point) above a horizontal axis.
It is similar to a bar graph but the display
still contains the original data values
51
Construct a Dot Plot for the following test
scores of 20 students.
60 70 90 65 70 70 80 90 85 80 85 85 85
90 70 65 95 85 95 100
52
Stem-and-leaf plots provide an easy way to sort
data.
Each number is separated into a stem
Similar to a bar graph but the display still
contains the original data values
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Stem-and-Leaf Plot Key
Key 4 5 45
Two digit data entries
Key 11 6 116
Three digit data entries
Data entries with 1 digit after the decimal
Key 12 3 12.3
Always use consecutive integers for stems.
If there is no data for a stem, the leaf part is
empty.
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Stem-and-Leaf Plot
Number of Minutes on the Internet
50 40 41 17 11 7 22 44 28 21 19 23
37 51 54 42 88 41 78 56 72 56 17 7
What stems should we use?
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Number of Minutes on the Internet
Key 1 6 16
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Number of Minutes on the Internet
50 40 41 17 11 7 22 44 28 21 19 23
37 51 54 42 88 41 78 56 72 56 17 7
57
Number of Minutes on the Internet
Key 1 6 16
Now, order the data
58
Number of Minutes on the Internet
Key 1 6 16
Does the Plot look like a bar graph?
59
Construct a stem-and-leaf plot and a dot plot for
the following data set. 80 52 90 52 53 55 70 82 9
1 55 55 71 82 74 91 82 74 55 75 85 93 85 93 76 56
76 93
60
Key 64 is 64
61
Practice A 2.1.B
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(No Transcript)
63
A time series graph is a line graph used to show
a pattern that occurs over a period of time
Horizontal axis year/month Vertical axis number
or percent
64
time series graph
gt gas prices each week for 3 months gt
students enrolled at RV gt winning times in an
Olympic race for the last 10 Olympics gt sales
each month of one year
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Month J F M A M J J A S O N D
Average price for a gallon of gas











2.40 2.30 2.20 2.10 2.00 1.90 1.80 1.70 1.60

J F M A M J J A S O N D
66
Practice A 2.1.C