 # Descriptive Statistics Summarizing qualitative data Summarizing quantitative data.

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Descriptive Statistics Summarizing qualitative data Summarizing quantitative data

Summarizing Qualitative Data The frequency distribution The relative frequency distribution The percent frequency distribution The pie graph The bar graph

Frequency Distribution A frequency distribution is a tabular summary of data showing the frequency (or number) of items A frequency distribution is a tabular summary of data showing the frequency (or number) of items in each of several nonoverlapping classes. in each of several nonoverlapping classes. The objective is to provide insights about the data that cannot be quickly obtained by looking only at that cannot be quickly obtained by looking only at the original data. the original data.

Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are : Marada Inn Example Below Average Average Above Average Above Average Above Average Below Average Below Average Average Average Poor Poor Above Average Above Average Excellent Excellent Above Average Above Average Average Average Above Average Above Average Average Average Above Average Above Average Average Average

Frequency Distribution Rating Poor2 Below Average3 Average5 Above Average9 Excellent1 Total20

Rows 9-21 not shown Using Excel’s COUNTIF function to construct a frequency distribution Formula Worksheet

Relative Frequency Distribution The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class.The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class. A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class.A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class.

Percent Frequency Distribution The percent frequency of a class is the relative frequency multiplied by 100.The percent frequency of a class is the relative frequency multiplied by 100. A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class.A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class.

Rows 9-21 not shown Using Excel’s COUNTIF function to construct a frequency distribution Value Worksheet

Relative Frequency and Percent Frequency Distributions Poor Below Average Average Above Average Excellent.10.15.25.45.05 Total 1.00 10 15 25 45 5 100 Relative RelativeFrequency Percent PercentFrequency Rating.10(100) = 10 1/20 =.05

Rows 9-21 and columns A-B are not shown Using Excel’s COUNTIF function to construct a percent frequency distribution Formula Worksheet

Rows 9-21 and columns A-B are not shown Using Excel’s COUNTIF function to construct a percent frequency distribution Value Worksheet

Bar graph These are used to display qualitative data. On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes.On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the vertical axis).A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the vertical axis).

Poor Below Average Below Average Above Average Above Average Excellent Frequency Rating Bar Graph 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 Marada Inn Quality Ratings The bars are separated to emphasize the fact that each class is a separate category.

Using Excel’s Chart Wizard to Construct Bar Graphs Step 1 Select cells C1:D6 Step 2 Click the Chart Wizard button Step 3 When the Chart Type dialog box appears: Choose Column in the Chart type list Choose Column in the Chart type list Choose Clustered Column from the Chart Choose Clustered Column from the Chart sub-type display Click Next > Click Next > Step 4 When the Chart Source Data dialog box appears Click Next > Click Next > … continued

Step 5 When the Chart Options dialog box appears: Using Excel’s Chart Wizard to Construct Bar Graphs … continued Select the Titles tab and then Type Marada Inn Quality Ratings in the Type Marada Inn Quality Ratings in the Chart title box Chart title box Type Quality Rating in the Value (X) axis box Type Quality Rating in the Value (X) axis box Type Frequency in the Value (Y) axis box Type Frequency in the Value (Y) axis box Select the Legend tab and then Remove the check in the Show Legend box Remove the check in the Show Legend box Click Next > Click Next >

Step 6 When the Chart Location dialog box appears: Specify the location for the new chart Specify the location for the new chart Click Finish to display the bar graph Click Finish to display the bar graph Using Excel’s Chart Wizard to Construct Bar Graphs

Soft Drink Demonstration Note: Excel file contained on text CD (Chapter 2--Softdrink

Pie Chart The pie chart is a commonly used graphical device The pie chart is a commonly used graphical device for presenting relative frequency distributions for for presenting relative frequency distributions for qualitative data. qualitative data. n First draw a circle; then use the relative frequencies to subdivide the circle frequencies to subdivide the circle into sectors that correspond to the into sectors that correspond to the relative frequency for each class. relative frequency for each class. n Since there are 360 degrees in a circle, a class with a relative frequency of.25 would a class with a relative frequency of.25 would consume.25(360) = 90 degrees of the circle. consume.25(360) = 90 degrees of the circle.

Below Average 15% Below Average 15% Average 25% Average 25% Above Average 45% Above Average 45% Poor 10% Poor 10% Excellent 5% Excellent 5% Marada InnQuality Ratings Marada Inn Quality Ratings Pie Chart

Note: Excel file contained on text CD (Chapter 2--Softdrink Soft Drink Demonstration