The Reading Log Inference
A class keeps a reading log. Each student records minutes read per night for one week. Maya's log shows: Mon 20, Tue 25, Wed 0, Thu 30, Fri 15, Sat 40, Sun 10. Her friend claims, "Maya read less than 20 minutes every night." Another says, "Maya read about 20 minutes a night on average." The teacher asks students to use the data to judge each claim and to decide what the log can and cannot tell us about Maya's reading habits.
1. Is the claim "Maya read less than 20 minutes every night" supported by the log? Use the data to explain.
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No. The claim says every night was under 20 minutes. The log shows Tue 25, Thu 30, Sat 40, all above 20. A single counterexample disproves an "every" claim, and there are three. The word "every" makes the claim strong; the data directly contradict it. A correct restatement would be "some nights were under 20 minutes" (Mon 20 is not under 20, but Wed 0, Fri 15, Sun 10 are). Students should notice that 20 itself is not "less than 20."
2. Compute the mean and median minutes. Which measure better supports the claim "about 20 minutes a night on average"? Explain.
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Sum = 20+25+0+30+15+40+10 = 140. Mean = 140 ÷ 7 = 20. Ordered data: 0, 10, 15, 20, 25, 30, 40. Median = 20 (middle value). Both mean and median equal 20, so "about 20 minutes a night on average" is well supported. However, the mean hides the 0-minute night and the 40-minute night; the data vary widely. The student should note that an average of 20 does not mean every night was near 20.
3. What can the log NOT tell us about Maya's reading? Give two limitations and explain why each matters.
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Limitations include: (1) The log does not say what Maya read or whether she understood it; minutes measure time, not comprehension. (2) It does not explain the 0-minute Wednesday - she may have been sick, or forgot to log. A zero could be missing data rather than no reading. (3) One week is a small sample; her habits may differ in other weeks. Each matters because conclusions about her as a reader would be overreach. The log supports statements about minutes logged that week, not about her ability or consistency in general.