An Average of 3.4 Days and 81 Customers Who Waited Over a Week: Describing 1,240 Home Deliveries Before Anyone Tests Anything
Student Name
American College of Education
STAT5003: Business Statistics: Data-Informed Decision-Making
Module 1 Assignment
Instructor Name
May 12, 2025
The Business Question and the Data
Riverbend Home Supply, the composite regional home goods retailer used in this course, delivers furniture, appliances and other large items from two distribution centers, North and South. Its website promises delivery in three to five days. The operations vice president has been reporting average delivery time each month, and the figure for the first quarter of 2025 was 3.4 days, comfortably inside the promise. Customer service, however, logged 96 complaints about late deliveries in the same quarter, more than double the previous year. The question for this module is simple: what do delivery times actually look like, and does the average describe them fairly?
The dataset contains every large-item home delivery completed between January 1 and March 31, 2025: 1,240 deliveries, 700 from North and 540 from South. Each record carries the order date, the delivery date, the distribution center, the carrier and the customer's ZIP code. Delivery time is measured in calendar days from order to delivery. No records were removed from the quarter's delivery file. Because the dataset is the full quarter rather than a sample, the figures below describe the quarter exactly; inference about future quarters is left to later modules. Before asking whether a number is significant, it is worth asking whether it is the right number.
One measurement choice deserves a note because it affects every figure. Delivery time counts calendar days, not business days, because the website's promise is read by customers as calendar days and because weekend deliveries are offered from both centers. Orders for items that were out of stock when ordered were already excluded by the company's system, which records them as backorders rather than deliveries. That exclusion means the figures describe how long delivery takes once an item is available, which is the part of the process the distribution centers control, and not the whole wait some customers experience.
Center
The mean delivery time for the quarter was 3.41 days, the figure the vice president reported. The median, the middle value when all deliveries are sorted, was 3 days, and the most common value was 2 days, recorded for 314 deliveries. The mean exceeds the median, which is the first sign that something is pulling the average upward. In a symmetric distribution, the two would be close.
For a manager, the median says that a typical customer received a delivery in three days, which fits the promise. The mean says less than it appears to, because it is influenced by every delivery, including a small number of very long ones. Neither number, on its own, tells the manager how many customers had a bad experience.
Spread and Shape
The standard deviation was 2.28 days, large relative to a mean of 3.41. The quartiles were 2 and 4 days, so the middle half of deliveries fell within a two-day range, which is tight. The 90th percentile was 6 days, and the longest delivery took 15 days. In the terms Tukey (1977) proposed for exploring data, the five-number summary of minimum, first quartile, median, third quartile and maximum is 1, 2, 3, 4 and 15. The distance from the third quartile to the maximum, 11 days, is more than five times the interquartile range, a clear mark of a long tail.
The frequency counts confirm it. Of the 1,240 deliveries, 986, or 79.5 percent, arrived within four days, and 1,159 arrived within seven. The remaining 81, or 6.5 percent, took eight days or more, with a cluster between 8 and 12 days. The distribution is strongly skewed to the right, with a skewness coefficient of about 2.0. Anscombe (1973) showed with four small datasets that identical means, variances and correlations can describe very different data, and argued that analysts should look at the data before trusting any summary. Here, a histogram of delivery days shows a tall, compact body and a separate low hump to the right, a shape that no single average could convey.
Where the Tail Comes From
A second hump in a distribution often means two different processes have been combined, so the deliveries were separated by distribution center. North's 700 deliveries had a mean of 2.80 days, a median of 3, a standard deviation of 1.37 and a maximum of 8; only 2 took more than a week. South's 540 deliveries had a mean of 4.20 days, a median of 3, a standard deviation of 2.90 and a maximum of 15; 79 of them, 14.6 percent, took more than a week. The medians are identical. The difference lies entirely in South's tail.
Separating South's deliveries by carrier explains the tail. South uses its own trucks for most customers but hands deliveries to rural ZIP codes to an outside carrier. The 462 deliveries on South's own trucks had a mean of 3.20 days and a standard deviation of 1.50, with 5 over a week. The 78 deliveries handed to the carrier had a mean of 10.14 days, a median of 10 and a standard deviation of 1.93; 74 of those 78 took more than a week. In other words, 74 of the 81 late deliveries in the quarter came from one carrier serving about 6 percent of customers. Every one of those customers was promised three to five days.
What the Manager Should Report
The monthly average is not wrong, but it answers the wrong question. It blends a fast, consistent process with a slow one serving a small group and reports a number that describes neither. Three changes would make the monthly report useful. First, report the median alongside the mean, since the median describes the typical customer and is not moved by the tail. Second, report the 90th percentile and the share of deliveries over seven days, since those describe the customers who complain. Third, report every measure separately for North, South's own trucks and the outside carrier.
The form of the report matters as well. Cleveland and McGill (1984) found that readers compare quantities best when the values sit at different points on one shared axis, and worst when they must compare angles or areas. A side-by-side box plot for the three delivery routes, on one axis of days, would let the vice president see in a single glance what the average has concealed. A pie chart of on-time and late deliveries would not.
What This Description Sets Up
Description has done its work: it located the problem before any test was run. It also sets up questions that later modules can answer with inference. Is the carrier's 10-day average likely to persist, or was the first quarter unusual? If Riverbend moved rural deliveries to its own trucks, how confident could it be about the resulting delivery times? And do rural customers who wait more than a week spend less with Riverbend afterward? All three reach past the quarter observed here, and each requires the probability and sampling tools of the modules that follow.
References
Anscombe, F. J. (1973). Graphs in statistical analysis. The American Statistician, 27(1), 17-21. https://doi.org/10.1080/00031305.1973.10478966
Cleveland, W. S., & McGill, R. (1984). Graphical perception: Theory, experimentation, and application to the development of graphical methods. Journal of the American Statistical Association, 79(387), 531-554. https://doi.org/10.1080/01621459.1984.10478080
Tukey, J. W. (1977). Exploratory data analysis. Addison-Wesley.
How this STAT 5003 Module 1 example is structured
STAT 5003 Module 1 often starts with describing a business dataset before any inference is attempted; your classroom's instructions decide the dataset and the software. This example states the business question and the data first, then reports center, spread and shape for the whole dataset, then breaks the data into the groups that explain its shape. Each statistic is followed by what it means for the business, and the paper ends by recommending which summary measures to report and why.
STAT5003 Module 1 questions, answered
What does STAT5003 Module 1 usually ask for?
STAT5003 Module 1 often asks students to describe a business dataset with measures of center, spread and shape before any inference, and to explain what the description means for a business decision. Your classroom's instructions decide the dataset and software.
When should I report the median instead of the mean?
When the data are skewed or have outliers, the median describes the typical case better, because it is not pulled by extreme values. Reporting both, with the reason they differ, is often the most informative choice.
Do I need a chart in a descriptive statistics assignment?
Usually yes. A histogram or box plot shows shape and outliers that summary numbers can hide, and research on graphical perception favors charts that place values along a common scale.
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