Section 3.1 ~
Frequency Tables
Introduction to Probability and Statistics
Ms. Young
Sec. 3.1
Homework Quiz
1.
2.
In what context is the term frequency referred to in this section?
a.
b.
Whether a radio is on AM or FM
The number of cycles per second in a wave motion
c.
The number of times data values fall into a category
Binning data is:
a.
b.
c.
3.
The percentage of values that fall into a certain category is referred to
as the:
a.
b.
c.
4.
Grouping data into categories covering a range of values
Excluding data from a data set
Estimating the frequency when dealing with large quantities of data
Cumulative frequency
Frequency
Relative frequency
The last category should have a cumulative frequency equal to:
a.
b.
The total number of data values
The first data value
c.
The frequency of the last category
Sec. 3.1
Objective

To be able to create and interpret frequency
tables
 Key




Terms:
Frequency Table
Binning
Relative Frequency
Cumulative Frequency
Sec. 3.1
Frequency Tables

A frequency table typically contains two columns:




A column listing the categories of the data
A column listing the number of data values (or frequency) that fall in that
category
Used to organize data that may fall into similar categories
Example
Professor Delaney records the following list of grades she gave to her 25
students on a set of essays:
 A C C B C D C C F D C C C
 B B A B D B A A B F C B
 Constructing a frequency table would be much easier to read

 The five possible letter grades (A, B, C, D, & F) are the categories
Grade
Frequency
A
4
B
7
C
9
D
3
F
2
Total
25
Total frequency should
equal the number of data
values you have
Sec. 3.1
Example 1

The Rocky Mountain Beverage Company wants feedback on its
new product, Coral Cola, and sets up a taste test with 20
people. Each individual is asked to rate the taste of the cola on
a 5-point scale:
(bad taste) 1 2 3 4 5 (excellent taste)
The 20 ratings are as follows:
13323343242353453431
Construct a frequency table for these data.
Taste
Scale
Frequency
1
2
2
3
3
9
4
4
5
2
Total
20
Sec. 3.1
Binning Data

A technique known as binning is used when there are a significant
amount of data values in which each value is different
It would be impossible or impractical to have a category for every value
 The data can be put into groups (or bins) that cover a range of values
 The following table represents a frequency table containing bins using the
data from P.91

Annual Energy per Person
(millions of BTUs)
Frequency (# of States)
200-299
300-399
400-499
500-599
600-699
700-799
800-899
900-999
1,000-1,099
1,100-1,199
TOTAL
16
19
10
1
1
0
1
1
0
1
50
Sec. 3.1
Example 2

For the 30 stocks of the Dow Jones Industrial Average, Table 3.5 (on
p.92) shows the annual revenue (in billions of dollars), the one-year
total return, and the rank on the Fortune 500 list of largest U.S.
companies. Create a frequency table for the revenue.
Since the revenues range from $21.6 billion to $351 billion, it would be
appropriate to span from $0 billion to $400 billion
 Bins with a $50 billion width would be appropriate
 Since the data values are given to the nearest tenth, your bins should be
representative of that

Annual Revenue
(billions of dollars)
Frequency
(number of companies)
0-49.9
13
50-99.9
10
100-149.9
3
150-199.9
1
200-249.9
1
250-299.9
0
300-349.9
1
350-399.9
1
Total
30
Sec. 3.1
Relative Frequency

The relative frequency for any category is the percentage of the
data values that fall in that category
relative frequency =

frequency in category
total frequency
A relative frequency table is created by simply adding a third column
containing the relative frequencies for each category

Ex. ~ Suppose Mr. Delaney wants to know the percentage of students that
received an A on the exam he gave. A relative frequency table allows for
quick reference to find this information.
Grade
Frequency
Relative Frequency
A
4
4/25 = .16 = 16%
B
7
7/25 = .28 = 28%
C
9
9/25 = .36 = 36%
D
3
3/25 = .12 = 12%
F
2
2/25 = .08 = 8%
Total
25
1 = 100%
Sec. 3.1
Cumulative Frequency

The cumulative frequency is the number of data values in that
category and all preceding categories
This is beneficial when you want to look at data such as grades to see how
many students received a C or better
 Cumulative frequencies only make sense for data categories that have a
clear order (data at the ordinal, interval, and ratio levels of measurement)

Grade
Frequency
Cumulative
Frequency
A
4
4
B
7
7+4=11
C
9
9+7+4=20
D
3
3+9+7+4=23
F
2
2+3+9+7+4=25
Total
25
25
Sec. 3.1
Example 3

Using the taste test data from Example 1, create a frequency table with
columns for the relative and cumulative frequencies. What percentage of
the respondents gave the cola the highest rating? What percentage gave
the cola one of the three lowest ratings?
Taste Scale
Frequency
Relative
Frequency
Cumulative Frequency
1
2
2/20 = .10 = 10%
2
2
3
3/20 = .15 = 15%
2+3=5
3
9
9/20 = .45 = 45%
2 + 3 + 9 = 14
4
4
4/20 = .20 = 20%
2 + 3 + 9 + 4 = 18
5
2
2/20 = .10 = 10%
2 + 3 + 9 + 4 + 2 = 20
Total
20
1= 100%
20
10% of the respondents gave the cola the highest rating
 14/20, or 70% of the respondents gave the cola one of the three lowest ratings

Sec. 3.1
Summary




Frequency tables are used to show the number of
values that fall into a certain category
Binning is used when it is impractical to reference
every value
The relative frequency is a percentage of the total
frequency for each category
The cumulative frequency is the total frequency for
that category as well as all the categories before it