Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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34 CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA TABLE 2.2 Atlanta Store Product Categories Frequency Distribution Number of Product Catagories Frequency 1 25 2 29 3 42 4 92 5 83 6 71 7 35 8 19 9 29 10 18 11 7 Total 450 TABLE 2.3 Frequency Distributions of Years of College Education Dallas Knoxville Years of College Frequency Years of College Frequency 0 35 0 187 1 21 1 62 2 24 2 34 3 22 3 19 4 31 4 14 5 13 5 7 6 6 6 3 7 5 7 4 8 3 8 0 Total 160 Total 330 Relative Frequency The proportion of total observations that are in a given category. Relative frequency is computed by dividing the frequency in a category by the total number of observations. The relative frequencies can be converted to percentages by multiplying by 100. of years of college attended. The responses ranged from zero to eight years. Table 2.3 shows the frequency distributions for each city. Suppose now we wished to compare the college years distribution for Dallas with that for Knoxville. How do the two cities’ distributions compare? Do you see any difficulties in making this comparison? Because the surveys contained different numbers of people, it is difficult to compare the frequency distributions directly. When the number of total observations differs, comparisons are aided if relative frequencies are computed. Equation 2-1 is used to compute the relative frequencies.
CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 35 Relative Frequency Relative frequency f i n (2.1) where: f i Frequency of the ith value of the discreate variable n k ∑ i1 f i k The number of different values for the discrete variable Table 2.4 shows the relative frequencies for each city’s distribution. This makes a comparison of the two much easier. We see that Knoxville has relatively more people without any college (56.7%) or one year of college (18.8%) than Dallas (21.9% <strong>and</strong> 13.1%). At all other levels of education, Dallas has relatively more people than Knoxville. The frequency distributions shown in Table 2.2 <strong>and</strong> Table 2.3 were developed from quantitative data. That is, the variable of interest was numerical (number of product categories or number of years of college). However, a frequency distribution can also be developed when the data are qualitative data or nonnumerical data. For instance, if a survey asked individuals for their marital status, the following possible responses could be listed: Single Married Divorced Other Table 2.5 shows the frequency distribution from a survey of 200 people. TABLE 2.4 Relative Frequency Distributions of Years of College Dallas Knoxville Years of Relative Relative College Frequency Frequency Frequency Frequency 0 35 35/160 0.219 187 187/330 0.567 1 21 21/160 0.131 62 62/330 0.188 2 24 24/160 0.150 34 34/330 0.103 3 22 22/160 0.138 19 19/330 0.058 4 31 31/160 0.194 14 14/330 0.042 5 13 13/160 0.081 7 7/330 0.021 6 6 6/160 0.038 3 3/330 0.009 7 5 5/160 0.031 4 4/330 0.012 8 3 3/160 0.019 0 0/330 0.000 Total 160 330 TABLE 2.5 Marital Status Frequency Distribution Marital Status Frequency Single 80 Married 90 Divorced 20 Other 10 Total 200
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Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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