3.1 Frequency Tables
LEARNING GOAL
Be able to create and interpret frequency tables.
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Definition
A basic frequency table has two columns:
• One column lists all the categories of data.
• The other column lists the frequency of each category,
which is the number of data values in the category.
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EXAMPLE 1 Taste Test
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.
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EXAMPLE 1 Taste Test
Solution:
The variable of interest is taste, and this variable can
take on five values: the taste categories 1 through 5.
(Note that the data are qualitative and at the ordinal
level of measurement.)
We construct a table
with these five
categories in the left
column and their
frequencies in the
right column, as
shown in Table 3.2.
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Binning Data
Definition
When it is impossible or impractical to have a category
for every value in a data set, we bin (or group) the data
into categories (bins), each covering a range of
possible data values.
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EXAMPLE 2 The Dow Stocks
For the 30 stocks of the Dow Jones Industrial Average,
Table 3.5 (previous slide) 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. Discuss the pros and cons
of the binning choices.
Solution: The revenue data range from $21.6 billion
(McDonald’s) to $351.1 billion (Wal-Mart). There are many
possible ways to bin data for this range; here’s one good way
and the reasons for it:
• We create bins spanning a range from $0 to $400 billion. This
covers the full range of the data, with extra room below the
lowest data value and above the highest data value.
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EXAMPLE 2 The Dow Stocks
Solution: (cont.)
• We give each bin a width of $50 billion so that we can span the
$0 to $400 billion range with eight bins. Also, the width of $50
billion is a convenient number that helps make the table easy
to read.
• Because the data values are given to the nearest tenth (of a
billion dollars), we also define the bins to the nearest tenth so
that they do not overlap. That is, bins go from $0 to $49.9
billion, from $50.0 to $99.9 billion, and so on.
Table 3.6 (on the next slide) shows the resulting frequency table.
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TIME OUT TO THINK
Consider three other possible ways of binning the data in
Table 3.6: 4 bins spanning the range $0 to $400 billion,
11 bins spanning the range $0 to $375 billion, and 36 bins
spanning the range $0 to $360 billion. Briefly discuss the
pros and cons of each of these choices.
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Relative Frequency
Definition
The relative frequency of any category is the
proportion or percentage of the data values that fall
in that category:
relative frequency =
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frequency in category
total frequency
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Cumulative Frequency
Definition
The cumulative frequency of any category is the
number of data values in that category and all
preceding categories.
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EXAMPLE 3 More on the Taste Test
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?
Solution: We find the relative frequencies by dividing the
frequency in each category by the total frequency of 20. We find
the cumulative frequencies by adding the frequency in each
category to the sum of the frequencies in all preceding
categories. Table 3.9 (on the next slide) shows the results.
The relative frequency column shows that 0.10, or 10%, of the
respondents gave the cola the highest rating.
The cumulative frequency column shows that 14 out of 20
people, or 70%, gave the cola a rating of 3 or lower.
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The End
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