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Notes pg12-22 - 12 Descriptive Statistics Tabular and...

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Descriptive Statistics: Tabular and Graphical Displays Both qualitative and quantitative variables can be displayed using tables and graphs. We will begin with tables and graphs for qualitative data. Summarizing Qualitative Data with Tables and Graphs Frequency Distribution. A frequency distribution is a table of data showing the number (or frequency) of items in each of several non-overlapping classes. Used for nominal or ordinal level data. As an example, let’s look at question number seven on p.33 of your textbook. This data represents ratings for Leverock’s Waterfront Steakhouse in Madeira Beach, Florida. Fifty customers were randomly sampled and asked to rate their dining experience at Leverock’s. The data are shown in the table below: G G O O O 12
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V A G G G V G P V O O V O O G O O V O V O O A V O A A V G O G O O O A V V O G V P V O A A O = outstanding V=very good G = good A = average P = poor Create two columns, one with the categories, one with the corresponding counts: Rating Frequency O 19 V 12 G 10 A 7 P 2 Total 50 Relative Frequency Distribution . Relative Frequencies reflect the proportion of the total number of observations that fall into each category. They are calculated as: Frequency of the class Relative frequency of a class = n 13
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The relative frequency distribution for the data is: Rating Rel. Freq. Rel. Freq. O 19/50= .38 V 12/50= .24 G 10/50= .20 A 7/50= .14 P 2/50= .1.00 Total 50/50 50 14
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Frequency Bar Charts are graphs of frequency distributions for qualitative data. They are created by plotting frequencies against corresponding categories or classes. For the restaurant data, we would have: Frequency Bar Chart 0 5 10 15 20 O V G A P Ratings Frequency Relative Frequency Bar Charts are created by plotting relative frequencies against corresponding categories or classes. For the restaurant data, we would have: 15
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Relative Frequency Bar Chart 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 O V G A P Ratings Relative Frequency Notice that the shapes of the distributions for the frequency and relative frequency bar charts are the same, only the vertical scale differs. Of course, we could easily convert the relative frequencies for our bar chart to percentages: 38% 24% 20% 14% 4% 0% 5% 10% 15% 20% 25% 30% 35% 40% O V G A P Ratings Percentages 16
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Pie Charts Like the bar chart, pie charts are used to depict qualitative data, data measured on either a nominal or ordinal scale. The relative frequencies of each category are depicted as proportionate slices of the pie. Usually, the proportions are multiplied by 100, so that they are displayed as percentages. Pie Chart for the Restaurant Data 17
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O 38% V 24% G 20% A 14% P 4% Another Example : The following table displays the occupancy numbers for Fayette College dormitories and off- campus housing. Housing Location Numb er Rel. Freq. Baker 250 0.12 Libby 300. 0.14 McPhie 187 0.09 Cooper 225 0.11 Pugh Towers 545 0.25 Ruffey 129 0.06 Off-Campus 505 0.24 Total 2141 1.00 The first two columns of the data comprise the ‘frequency distribution’. The first and third 18
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columns comprise the ‘relative frequency distribution’. Notice that the relative frequency
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