The research firm LL Research collected data from 200 client businesses. They want to determine how the businesses compare among four variables:
2015 Profit in millions of dollars
2016 Profit in millions of dollars
2015-2016 Two-Year Change in Daily Average Customer Visits
Two-Year Average Number of Employees
Data collected for the sample of 200 businesses is contained in the file named Businesses. Be sure to use all 200 data points.
Prepare a report (see below) using the numerical methods of descriptive statistics presented in this module to learn how each of the variables contributes to the success of a client’s business. Be sure to include the following three items in your report.
Compute descriptive sample statistics (mean, median, two quartiles Q1 and Q3 (using QUARTILE.EXC), minimum, maximum, range, interquartile range, sample standard deviation, and coefficient of variation) for each of the four variables along with an explanation of what the descriptive statistics tell us about the client businesses.
In this case, which measure of central tendency would be best for this application? Explain why.
Which measure of variation would be best for this application? Explain why.
How can one use the above descriptive statistics to understand the businesses better?
Which graphical displays of data would you use to help understand or complement the above descriptive statistics? Explain how and why.
Note: QUARTILE.EXC works only for Excel 2010 or newer.
Compute the percent change in profit from 2015 to 2016 for each business.
What would the percent change tell us in this application?
Then use the z-score to determine which businesses were outliers with respect to percent change in profit.
- How would identifying outliers be useful in this application?
What advice might you give to businesses that are outliers?
- How else would you determine outliers?
- Compute the sample correlation coefficient, showing the relationship between percent change in profit and each of the other two variables (2015-2016 Two-Year Change in Daily Average Customer Visits and Two-Year Average Number of Employees).
- Explain what the correlation coefficients tell us about the three pairs of relationships. Use tables, charts, or graphs to support your conclusions.Â