DDBA 8307B Week 2 Distribution Write-Up Example

Putting the Shape Back Into Words: A Distribution Write-Up of a Year of Invoice Payment Times at a Building-Supply Wholesaler, Describing the Typical Invoice, the Spread, the Values That Looked Wrong and What Was Done With Each

Student Name

Walden University

DDBA 8307B: Quantitative Business Data Analysis Using SPSS

Instructor Name

Month Day, Year

Putting the Shape Back Into Words: A Distribution Write-Up of a Year of Invoice Payment Times at a Building-Supply Wholesaler, Describing the Typical Invoice, the Spread, the Values That Looked Wrong and What Was Done With Each

The Data

The data are payment times for every invoice issued in fiscal 2025 by a composite building-supply wholesaler in Atlanta that sells lumber, roofing and drywall to about 1,300 contractor accounts on 30-day terms. Payment time is the number of days from the invoice date to the date payment was posted. The file holds 8,412 invoices. The controller wants to know how long customers take to pay. An average alone would answer that badly, so this write-up describes the shape of the distribution and explains every value that looked wrong before it was summarized.

Values That Looked Wrong, and What Was Done

Each odd value was investigated before a decision was made. Tukey (1977) urged analysts to look at data before summarizing it, because a single wrong value can distort a summary and a single real but extreme value can be the most important thing in the data. Correcting the 17 negative values used a second record, the delivery date. Keeping the 212 zero-day invoices recognizes that counter sales are part of the business. Setting aside the 23 unpaid invoices avoids treating "never paid" as a number of days; they will be reported as a separate count. Keeping the nine very late invoices recognizes that disputes happen, but flagging them lets the reader see how much they move the summary.

Table 1

Odd Values and Their Treatment

Each treatment confirmed with the accounts receivable supervisor before analysis.

The Shape

After corrections, 8,389 invoices have payment times. The distribution has a long right tail: most invoices are paid within a few weeks of the 30-day due date, and a long tail stretches out past two months.

The typical invoice is paid in about 34 days, four days after the due date. Half of invoices fall between 26 and 49 days. The mean of 41.6 days is pulled up by the long tail and describes almost no actual invoice. Field (2018) recommends the median and interquartile range for skewed distributions, and this write-up follows that advice. Without the nine disputed invoices, the median is unchanged and the mean falls to 40.4 days, which shows the tail has more effect on the mean than on the typical case.

Table 2

Summary of Payment Times in Days (n = 8,389)

Computed in SPSS Explore; the nine invoices over 365 days included.

What the Shape Suggests

The histogram in SPSS showed a second, smaller bump around 60 to 70 days. Looking at which accounts produced it, about 80 percent of those invoices came from 42 accounts that pay every invoice roughly two months late. They are not random late payers; they are customers who have, in effect, set their own terms. That is a finding the controller can act on, and it would have been invisible in an average.

How the Write-Up Was Produced in SPSS

The distribution was examined with the Explore procedure, which produced the summary statistics, a histogram, a box plot and a stem-and-leaf display. The box plot flagged 312 invoices as outliers above the upper fence, but nearly all of them were real late payments rather than errors, so they were kept; outlier flags in a skewed distribution often mark the tail rather than mistakes. The 999 code was declared as missing in Variable View before any statistics were run, so it could not inflate the mean. Each decision is recorded in a syntax file, so the same steps can be repeated on next year's invoices.

What the Write-Up Does Not Show

The data cannot explain why customers pay late. They show when. Payment timing may reflect customers' own cash flow, disputes about deliveries or the wholesaler's collection effort, none of which is in the file. Appelbaum et al. (2018) recommend that reports state how data were cleaned and what was excluded, so readers can judge the results; the table of odd values serves that purpose here.

References

Appelbaum, M., Cooper, H., Kline, R. B., Mayo-Wilson, E., Nezu, A. M., & Rao, S. M. (2018). Journal article reporting standards for quantitative research in psychology: The APA Publications and Communications Board task force report. American Psychologist, 73(1), 3-25. https://doi.org/10.1037/amp0000191

Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). SAGE Publications.

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