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# Descriptive Statistics: Box and Whisker Plot

The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The variables in the survey can be found in the file CODING.

We will concentrate on variables 18-25, which reflect how important each of eight different attributes is in the respondent's selection of a shopping area. Each of these variables has been measured on a scale of 1 ("1" means the attribute is not very important in choosing a shopping area) to 7 ("7" means the attribute is very important in choosing a shopping area). The attributes being rated for importance are listed below. Examining the relative importance customers place on these attributes can help a manager "fine-tune" his or her shopping area to make it a more attractive place to shop.

18 Easy to return/exchange goods
19 High quality of goods
20 Low prices
21 Good variety of sizes/styles
22 Sales staff helpful/friendly
23 Convenient shopping hours
24 Clean stores and surroundings
25 A lot of bargain sales

1.Perform the following operations for variables 18-25:
- A. Obtain descriptive statistics (5-number summary, mean, mode, range and standard deviation) for each variable along with an explanation of what the descriptive statistics tell us about the variable.
- B. Generate a box-and-whisker plot for the variable. Does the distribution appear to be skewed? If so, is the skewness positive or negative? Calculations are easier for a quick check.
2. Based on the results for question 1, which attributes seem to be the most important and the least important in the respondents' choice of a shopping area? Which items from #1 did you use to decide on the least and most important attributes and why?
3.Use their respective coefficients of variation to compare the relative amount of dispersion in variable 29 (number of persons in the household) with that of variable 30 (respondent's age).
4.Determine the coefficient of correlation between variable 29 (number of persons in the household) and variable 30 (age). What percentage of the variation in household size is explained by respondent age?
Be sure that your report contains the following:

#### Solution Summary

This solution illustrates how to construct a Box and Whisker Plot for several variables, as well as determine the correlation coefficient and 5-number summary. A Word document and Excel file are attached and contain the solution.

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