Reporting Homework Hours Without Misleading the Board
Mr. Boone’s seventh graders surveyed 25 classmates about nightly homework and must present the results to the school board in a three-minute slot. The class has one 45-minute period left to finalize its slide. Results: median 1.5 hours, mean 2.4 hours, interquartile range 1 to 3 hours, and a full range of 0.5 to 12 hours. The 12-hour response came from a student who later said it included weekend assignments. The principal has already drafted a slide with two bars, “district average 1.6 hours” and “our school 2.4 hours,” drawn on a vertical axis that begins at 1.0 hour, so the school bar looks roughly five times taller. Students are arguing about whether to drop the 12-hour response and whether the mean or the median is the honest number to report.
1. Should the class drop the 12-hour response, and which measure of center should it report? Justify both decisions.
Read the worked answer
Fix the measurement first, then choose the summary.
The 12-hour response is not a lie and not an outlier to delete - it answers a different question, because the student included weekend assignments. Ask for a weekday-only figure and recompute. If it changes, the honest fix is a corrected value, not an excluded one. Deleting a value because it moves the mean is a decision made to protect a conclusion; the class must be able to justify any removal in terms of what the value measures, not what it does to the average.
If the value stands, report the median (1.5 h) as the typical load. With n = 25, one extreme pulls the mean by roughly (12 − 1.5)/25 ≈ 0.4 hours on its own. Report the mean alongside with that caveat, or omit it if the distribution is this skewed.
The board sentence: “The typical student reports about 1.5 hours on a weeknight; the mean is higher because a few students report much more.”
2. Identify what is misleading about the principal’s draft slide and specify how to redraw or replace it.
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The axis is the distortion. Truncating a bar-chart axis at 1.0 hour makes a 1.6 → 2.4 difference - a 50% increase - render as a bar roughly five times taller, because bar length is read as a ratio measured from zero. The graphic is not exaggerating the numbers; it is encoding the wrong quantity.
Two acceptable fixes:
- Zero baseline. Redraw with the axis running 0 to 3 hours. The bars then differ by 50%, which is the real claim and is still a meaningful difference.
- Change the form. If 0.8 hours is the story, say it: “about 48 minutes more per night.” A dot plot of the 25 responses preserves the spread and shows the skew - more informative than two bars and much harder to misread.
Also label n = 25, label the data as self-report, and make sure both figures are the same statistic. The draft compares a “district average” to a school mean without saying whether the district figure is a mean or a median; mixing them manufactures a comparison.
3. A board member asks, “So what is the typical homework load?” Write the response and explain why a single number is insufficient.
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Give a center and a spread, and state what the number rests on.
“Our best single estimate is a median of about 1.5 hours per weeknight. But the middle half of students report between 1 and 3 hours, and responses run from 30 minutes to 12 hours, so ‘typical’ hides a lot. The 12-hour response included weekend work, which we’re flagging.”
Why not one number: with 25 self-reported values, a single figure implies a precision the data do not have, and a board member will make policy from it. The interquartile range is the honest companion - it says how much students differ, which is the more actionable finding. A subgroup consistently reporting three or more hours is worth investigating; a school-wide average of 2.4 does not reveal that subgroup.
State the limits out loud as well: self-report, one question, 25 students, no check on how students counted time. Naming the limitations protects the class’s credibility more than a tighter-sounding number would.