Would you prefer the IQR instead of the standard deviation to describe this variable’s dispersion? Why or why not?
Pastas R Us, Inc. is a fast-casual restaurant chain specializing in noodle-based dishes, soups, and salads. Since its inception, the business development team has favored opening new restaurants in areas (within a 3-mile radius) that satisfy the following demographic conditions:
Median age between 25 and 45 years old
Household median income above national average
At least 15% college-educated adult population
Last year, the marketing department rolled out a loyalty card strategy to increase sales. Under this program, customers present their loyalty card when paying for their orders and receive some free food after making 10 purchases.
The company has collected data from its 74 restaurants to track important variables such as average sales per customer, year-on-year sales growth, sales per sq. ft., loyalty card usage as a percentage of sales, and others. A key metric of financial performance in the restaurant industry is annual sales per sq. ft. For example, if a 1,200 sq. ft. restaurant recorded $2 million in sales last year, then it sold $1,667 per sq. ft.
Executive management wants to know whether the current expansion criteria can be improved; evaluate the effectiveness of the loyalty card marketing strategy; and identify feasible, actionable opportunities for improvement. As a member of the analytics department, you’ve been assigned the responsibility of conducting a thorough statistical analysis of the company’s available database to answer executive management’s questions.
Part1 : Descriptive Statistics Analysis
Conduct the following descriptive statistics analyses using the PastasR Us, Inc. data set in Microsoft Excel. Answer the questions in the spreadsheet or a separate Microsoft Word document.
Insert a new column in the database that corresponds to AnnualSales. AnnualSales is the result of multiplying a restaurant’s SqFt by Sales/
Calculate the following:
mean
skew
5-number summary
interquartile range (IQR) for each of the variables
Create a box-plot for the AnnualSales variable and answer the following questions:
Does it look symmetric?
Would you prefer the IQR instead of the standard deviation to describe this variable’s dispersion? Why or why not?
Create a histogram for the Sales/SqFt variable and answer the following questions:
Is the distribution symmetric? If not, what is the skew?
Are there any outliers? If so, which one(s)?
What is the SqFt area of the outlier(s)? Is the outlier(s) smaller or larger than the average restaurant in the database? What can you conclude from this observation?
What measure of central tendency is more appropriate to describe Sales/SqFt? Why?
Answer preview Would you prefer the IQR instead of the standard deviation to describe this variable’s dispersion? Why or why not?
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