GB513 Unit 1 Descriptive Statistics Exercise Example

Where Free Delivery Should Start: A Unit 1 Descriptive Statistics Exercise on 200 Invoices

[Student Name]

Purdue University Global

GB513: Business Analytics

Unit 1 Descriptive Statistics Exercise

[Instructor Name]

[Date]

The restaurant supply distributor, its invoices and every figure are composite and illustrative; the methods cited are real.

The Question and the Data

Harbor Street Restaurant Supply delivers kitchen supplies, paper goods and dry food to restaurants, cafes and hotels. It now delivers every order free, at an average cost to the company of about $38 per delivery. Management wants to set a minimum order for free delivery and charge a fee below it. The file holds 200 invoices from the last quarter, one row per order, with the order value in dollars.

Summary Statistics

The Descriptive Statistics tool in Excel's Analysis ToolPak produced the summary below, trimmed to the measures a manager reads. David Levine, David Stephan and Kathryn Szabat recommend reporting the median and quartiles alongside the mean whenever a business data set may be skewed (Levine et al., 2021).

Count: 200 orders.

Mean: $311.29.

Median: $219.66.

Standard deviation: $316.17.

Minimum: $46.59. Maximum: $2,265.00.

First quartile: $150.54. Third quartile: $347.40.

The mean sits about $92 above the median, and the spread, measured by standard deviation, even exceeds the mean itself. Both point to a distribution stretched to the right by a few very large orders.

Histogram

A histogram with equal $100 bins, titled "Most orders fall between $100 and $400," shows a tall cluster from $100 to $400 and a long thin tail to the right. Only a handful of orders exceed $1,000. David Anderson and colleagues note that when a distribution is skewed, the median describes a typical value better than the mean (Anderson et al., 2020). Here, the typical order is close to $220, not $311.

Box Plot

A box plot, titled "Six hotel orders sit far beyond the rest," places the box from $150.54 to $347.40 with the median line at $219.66. John Tukey's box plot convention flags any point beyond 1.5 times the interquartile range past the third quartile (Tukey, 1977). The interquartile range is $196.86, so the upper fence is $642.70, and 15 orders lie above it. Six of those, between $1,480 and $2,265, came from two hotel accounts placing quarterly bulk orders. Without those six, the mean falls to $264.15, much closer to the median.

The mean is pulled up by two hotel accounts, so a threshold set at the mean would describe almost nobody's order.

Interpretation

For a delivery threshold, the question is what share of customers would clear it. About 43.5 percent of orders are $250 or more, and about 31 percent are $300 or more. A threshold at the mean of $311 would charge a fee on roughly 70 percent of orders, which would likely upset the small restaurants that make up most of the customer base. A threshold near the median would charge about half.

What the Spread Means for Delivery Cost

Delivery cost does not depend much on order value. A $60 order and a $600 order take the same truck stop, about $38 of driver time, fuel and vehicle cost. That means small orders are expensive to serve relative to what they bring in. The bottom quartile, the 50 orders below $150.54, carries a delivery cost equal to at least a quarter of each order's value, and for the smallest orders more than half. The third quartile, $347.40, shows that a quarter of customers place orders large enough that delivery cost is about a tenth of the order or less. The spread between those quartiles, not the average, is what the fee needs to address.

Checking the Result Without the Hotel Orders

Because the two hotel accounts behave differently from restaurants, the summary was rerun without their six orders. The median barely moves, falling by only a few dollars, because the median depends on the middle of the distribution rather than its tail. The mean falls by about $47. That confirms the median is the stable figure to build a policy on, while the mean would shift every time a large account placed a bulk order.

Limits

One quarter of invoices may not represent the year, since restaurants order differently in summer and during holidays. The analysis also treats each invoice as a separate customer, although some restaurants order several times a week. A follow-up should group invoices by customer to see how many accounts the fee would actually affect.

Recommendation

Harbor Street should set free delivery at $200, just below the median of $219.66, and charge a $15 fee on smaller orders. About 59 percent of orders are already $200 or more and would see no change. The fee would apply mainly to the bottom quartile, orders under about $150, which cost the most to deliver relative to their value. Customers just below $200 would have a reason to add an item. The recommendation rests on the median and the first quartile, which describe typical orders better than the mean in this skewed distribution. Management should review the threshold after one quarter, comparing the new median order with this one.

References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2020). Statistics for business and economics (14th ed.). Cengage.

Levine, D. M., Stephan, D. F., & Szabat, K. A. (2021). Statistics for managers using Microsoft Excel (9th ed.). Pearson.

Tukey, J. W. (1977). Exploratory data analysis. Addison-Wesley.