The Cafeteria Wait-Time Outlier
Mr. Okafor's grade-6 class collected cafeteria wait times for five days. Each pair timed 10 students, producing 50 times. One pair recorded a wait of 2 minutes on Tuesday; the line monitor says that day had a fire drill and the actual wait was about 22 minutes. The class entered the data into a spreadsheet. The mean is 9.8 minutes; the median is 8.5; the range is 20. A student's formula =AVERAGE(B2:B51) includes a blank cell and returns 10.0. Another student wants to delete the 2-minute value because 'it makes the graph ugly.' The principal will use the class's summary in a newsletter and asks for one 'average.' Mr. Okafor wants students to understand which measure of center to report, how outliers affect summaries, and how to check spreadsheet formulas. He has one 50-minute class and no additional technology support. The school newsletter deadline is tomorrow.
1. What should the class do with the 2-minute entry, and how should Mr. Okafor handle the spreadsheet discrepancy?
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The class should not delete the 2-minute value to make the graph look better. The entry is a data-quality problem: the line monitor reports a fire drill and an actual wait of about 22 minutes. Students should correct the value to 22, record why the correction was made, and recompute the summary. If all other values stay the same, the mean rises by 20/50 = 0.4 minute, from 9.8 to 10.2; the median may or may not shift, so students must check the ordered list rather than assume. The spreadsheet discrepancy is a separate audit lesson: a return of 10.0 instead of 9.8 signals that the range, the denominator, or a blank cell needs checking. Students should inspect whether the formula covers all 50 data cells and whether a blank is being treated as zero. Mr. Okafor should ask, 'What does the spreadsheet count as a data point?' This turns a technical glitch into evidence about how technology can hide assumptions.
2. What summary should the class give the principal, and how should students justify it?
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The class should give the principal context rather than a single bare number. After correcting the fire-drill value, report the mean and median, and note that Tuesday included a fire drill that produced an unusually long wait. The median is useful because it is resistant to extreme values; the mean is useful because it uses all the data and reflects total wait time. If the principal insists on one 'average,' the median is the better typical value for a skewed wait-time distribution, but the class should label it as the median and explain the fire-drill context. Students should not say the 22-minute value is an outlier to be discarded; it is a legitimate observation caused by a known event. The justification should include the corrected mean, the median, and a sentence about why the choice depends on the question the newsletter is answering: typical experience versus total minutes of waiting.
3. Design a 50-minute instructional sequence that uses this situation to teach measures of center, outliers, and spreadsheet checking.
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Start with a 7-minute launch: display the claim 'Delete the 2 because it makes the graph ugly' and ask pairs to write one reason for and one against. Next, 12 minutes: groups correct the data entry, document the fire drill, and recompute mean and median by hand or with a calculator; they record whether each measure changed and why. Then 12 minutes: groups compare a dot plot before and after correction and write a two-sentence recommendation for the principal, naming the question the summary answers. Next, 10 minutes: a spreadsheet audit station. Give groups a formula range with a blank cell and ask them to find what the technology is counting; students revise the formula or the data table. Finish with an 8-minute whole-class synthesis and a 3-minute exit ticket: 'A news story says the average wait is 10.2 minutes. Is that a typical wait? Explain using median, mean, and the fire drill.' This sequence keeps the judgment call at the center and uses the deadline as a real audience constraint.