Two Reading-Log Averages and a Misleading Graph
Two seventh-grade classes record weekly reading-log minutes. Class 1 (7 students): 12, 15, 14, 13, 40, 11, 15. Class 2 (7 students): 16, 17, 15, 16, 18, 15, 17. The 40 belongs to one student who logged a weekend read-a-thon, and the teacher confirms the entry is accurate. The school newsletter prints a bar graph of the two class averages with the vertical axis starting at 10 minutes rather than 0, under the headline "Class 1 Reads Less." A parent emails that the graph "proves" Class 1 is behind and asks the principal to assign Class 1 twenty extra minutes of homework.
1. Compute the mean and median for each class. Then state which measure answers the parent's question and which answers a different question.
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Class 1: sum = 12 + 15 + 14 + 13 + 40 + 11 + 15 = 120. Mean = 120 ÷ 7 ≈ 17.1 min. Ordered: 11, 12, 13, 14, 15, 15, 40 → median = 14 min.
Class 2: sum = 16 + 17 + 15 + 16 + 18 + 15 + 17 = 114. Mean = 114 ÷ 7 ≈ 16.3 min. Ordered: 15, 15, 16, 16, 17, 17, 18 → median = 16 min.
Which measure fits which question: "How many minutes does a typical Class 1 student log?" is answered by the median (14), because the single 40-minute entry is a legitimate outlier that pulls the mean above every student except that one - six of seven Class 1 students logged 15 minutes or less. "How many total minutes did the class log, per student on average?" is answered by the mean (17.1), which is the right figure for a total-minutes question.
Note that the means reverse the headline's claim: Class 1's mean (17.1) is higher than Class 2's (16.3), while the medians say the opposite (14 vs. 16). The choice of measure decides the answer.
2. Evaluate the headline and the graph's vertical axis. What should the newsletter report instead, and how should the principal respond to the homework request?
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The axis: starting the vertical axis at 10 min rather than 0 compresses the space available to the bars and exaggerates the visual gap between two values that differ by less than one minute. Readers perceive a large difference where the numbers show about 0.8 min.
The headline: "Class 1 Reads Less" is unsupported as stated. It is true of the median (14 < 16) but false of the mean (17.1 > 16.3). A headline that picks one measure without saying which is misleading regardless of the axis.
Better reporting: show medians with the axis from 0, state the spread, and disclose the outlier - for example: "Typical weekly minutes: Class 1, 14; Class 2, 16. One Class 1 student logged 40 minutes at a read-a-thon." That is accurate and still informative.
Principal's response: deny the intervention as stated. A 2-minute median difference in one week of self-reported logs from 7 students per class cannot justify 20 extra minutes of homework for a whole class, and the request rests on a graph artifact plus a measure choice that reverses the result. Suggest instead collecting several weeks of data and looking at the distribution before changing assignments.