Interpreting a School Survey on Screen Time
A Grade 10 class surveys 200 students about daily screen time. Results: mean 4.2 hours, median 3.5 hours, standard deviation 1.8 hours. The distribution is right-skewed because a few students report over 10 hours. A newspaper claims 'the average student spends over 4 hours a day on screens'. A student counters that 'half of students are below 3.5 hours, so the claim is misleading'. The teacher asks the class to evaluate both statements statistically, and also to consider a follow-up sample of 40 students whose mean was 4.8 hours.
1. Evaluate the newspaper's claim and the student's counter-claim using the mean, median, and skew.
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The newspaper uses the mean (4.2 h), which is pulled upward by the right-skewed high values. It is technically true that the arithmetic mean exceeds 4 hours, but 'the average student' suggests a typical student, which the median (3.5 h) better represents.
The student is correct that the median splits the data: about 50% of students report below 3.5 hours. However, saying 'the claim is misleading' is a fair criticism of wording, not proof the mean is wrong - the mean genuinely is 4.2 h.
Best conclusion: the typical student is closer to 3.5 h; the mean is inflated by a small tail of heavy users. Both statements contain a truth but neither is a complete description.
2. The follow-up sample of 40 students had mean 4.8 h. Using the population standard deviation of 1.8 h, compute a 95% confidence interval and judge whether it is consistent with the original mean of 4.2 h.
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Standard error = σ/√n = 1.8/√40 ≈ 1.8/6.3246 ≈ 0.2846 h.
95% CI: 4.8 ± 1.96 × 0.2846 = 4.8 ± 0.5578, giving approximately (4.24, 5.36) hours.
The original mean of 4.2 h lies just below the lower bound (4.24), so it is marginally outside the interval. This suggests the follow-up sample may come from a group with a slightly higher mean, or the difference could be sampling variation at the boundary.
Caveat: assuming σ = 1.8 for the new sample may be unjustified if the group differs. A cautious conclusion: there is weak evidence of a difference, and a larger sample would be needed to confirm it.