Example Of Managerial Report Using Several Types Of Statistics Report

Introduction

In this paper statistics and probability theory will be used to monitor the dynamics of shoes sales in Beltway Shoe Company. The company record original price of shoes, sale price and number of days it takes to sell each unit. There are two regions of selling in the United States – Eastern Region and Western Region. The report summarizes the assessments of the nature of the shoe market in each region.

Body

We are given with the data set of 100 observations which represent sales in Western and Eastern Regions in the United States (50 in Western and 50 in Eastern). The data is measured with the following variables:

List Price – the original price of the shoes

Sale Price – the sale price of the shoes
Days to Sell – the number of days it takes to sell each unit.
Start with descriptive statistics for each of three variables and both regions. The Excel output is below:
It is known that the data value may be considered as outlier is it is 1.5*IQR lower than 1st quartile or 1.5*IQR above 3rd quartile. Performing all calculations in Excel, there are the following Lower and Upper limits of the data which is considered as “usual”. All observations outside this interval are outliers.
Consider the difference between both regions. The typical original price is almost equal for both regions (109.78 for Western and 108.62 for Eastern). However, typical sale price in Eastern Region is 85.24 and in Western it is only 80.44. The usual amount of days to sell is also almost equal for both regions (62.68 and 62.36). Western Region data is more dispersed for each of three variables, because the indicators of standard deviation and sample variance are higher than in Eastern Region.
The next step of this research is to calculate 90% confidence interval estimate of the population mean sales price and population number of days to sell for both regions. As it known, 90% CI for mean is determined in the following way:

X±1.645*sn

All calculations are given in Excel and represented in the table below:
The obtained confident intervals may be interpreted in the following way:
“We are 95% confident that in Western Region the population mean of original price is between $103.28 and $116.28, the population mean of sale price is between $74.18 and $86.71, the population mean of days to sell is between $52.26 and $73.10. We are 95% confident that in Eastern Region the population mean of original price is between $103.76 and $113.48, the population mean of sale price is between $39.72 and $90.76, the population mean of days to sell is between $52.93 and $71.79.”

Margin of error of 90% confidence may be found by using the following formula:

ME=1.645*sn
If the manager requested estimates the mean selling price in Western Region with a margin of error of $5 and in Eastern Region with a margin error of $4, the sample sizes may be obtained from the formula above. Use Gold Seek function in Excel to find the value of the sizes:

The sample in Eastern Region should consist of 95 observations, the sample in Western Region should consist of 79 observations.

It is known that mean original price in Western Region is $81.25; the mean sale price is $58.5. In Eastern Region the mean original price is $94.25; the mean sale price is $65.75. The percent difference for the sale price and list price is:
Eastern Region=1-65.7594.25≈0.3024=30.24%Western Region=1-58.581.25=0.28=28%

Thus, if manager placed a pair of shoes in Western Region with original price of $120, the sale price will be:

120*1-0.28=$86.4

If manager placed a pair of shoes in Eastern Region with original price of $125, the sale price will be:

125*1-0.3024=$87.2
The approximate number of days to sell might be obtained from the list of observations for each region. There is a pair of shoes in Western Region was put on sale with original price of $120 and its number of days to sell was 74 days (highlighted with yellow in .xlsx file). Analogically, a pair of shoes in Eastern Region was priced of $125 and sold in 45 days. These numbers may serve as approximated number of days to sell for new pairs which were just placed on display.

References

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., & Cochran, J.J. (2015). Essentials of statistics for business and economics. (7th ed.). Stamford, CT: Cengage Learning.
Gut, Allan (2013). Probability: A Graduate Course (2 ed.). New York, NY: Springer. ISBN 978-1-4614-4707-8.
Gillies, Donald (2000); "Philosophical Theories of Probability"; Routledge; Chapter 4 "The subjective theory"