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Section 3.1 ~ Frequency Tables Introduction to Probability and Statistics Ms. Young

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Homework Quiz Sec. 3.1 1.In what context is the term frequency referred to in this section? a.Whether a radio is on AM or FM b.The number of cycles per second in a wave motion c.The number of times data values fall into a category 2.Binning data is: a.Grouping data into categories covering a range of values b.Excluding data from a data set c.Estimating the frequency when dealing with large quantities of data 3.The percentage of values that fall into a certain category is referred to as the: a.Cumulative frequency b.Frequency c.Relative frequency 4.The last category should have a cumulative frequency equal to: a.The total number of data values b.The first data value c.The frequency of the last category

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Objective Sec. 3.1 To be able to create and interpret frequency tables Key Terms: Frequency Table Binning Relative Frequency Cumulative Frequency

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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 Sec. 3.1 GradeFrequency A4 B7 C9 D3 F2 Total25 Total frequency should equal the number of data values you have

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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: 1 3 3 2 3 3 4 3 2 4 2 3 5 3 4 5 3 4 3 1 Construct a frequency table for these data. Sec. 3.1 Taste Scale Frequency 12 23 39 44 52 Total20

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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 Sec. 3.1 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 0 1 0 1 50

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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 Sec. 3.1 Annual Revenue (billions of dollars) Frequency (number of companies) 0-49.913 50-99.910 100-149.93 150-199.91 200-249.91 250-299.90 300-349.91 350-399.91 Total30

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Relative Frequency The relative frequency for any category is the percentage of the data values that fall in that category 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. Sec. 3.1 GradeFrequencyRelative Frequency A44/25 =.16 = 16% B77/25 =.28 = 28% C99/25 =.36 = 36% D33/25 =.12 = 12% F22/25 =.08 = 8% Total251 = 100%

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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) Sec. 3.1 GradeFrequencyCumulative Frequency A44 B77+4=11 C99+7+4=20 D33+9+7+4=23 F22+3+9+7+4=25 Total25

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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? 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 Taste ScaleFrequencyRelative Frequency Cumulative Frequency 122/20 =.10 = 10%2 233/20 =.15 = 15%2 + 3 = 5 399/20 =.45 = 45%2 + 3 + 9 = 14 444/20 =.20 = 20%2 + 3 + 9 + 4 = 18 522/20 =.10 = 10%2 + 3 + 9 + 4 + 2 = 20 Total201= 100%20

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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 Sec. 3.1

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