Problem 10 · 2019 AMC 8
Medium
Arithmetic & Operations
careful-counting
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Answer: B — Mean +1, median +1.
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Hint 1 of 2
You don't need to recompute either statistic from scratch — just track the change. Only one number moved, so what does adding to it do to the average, and where does it land in the sorted order?
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Hint 2 of 2
Mean: a bump of +5 spread over 5 days raises the average by 5÷5 = 1. Median: re-sort and watch whether the bumped value jumps past the old middle value.
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Approach: measure the shift in each statistic, don't recompute
- Only Wednesday changes, 16 → 21, so the total goes up by 5. Mean of 5 days rises by 5÷5 = 1 — no need to add the whole column.
- For the median, sort instead of recomputing. Originally 12, 16, 20, 24, 26, median 20. Raising 16 to 21 slides that value rightward past 20: new order 12, 20, 21, 24, 26, median 21. Median rises by 1.
- So both increase by 1.
- Why this transfers: changing one data value shifts the mean by (change ÷ count), but the median only moves if the changed value crosses the old middle — always re-sort to check, since the median can stay put even when the mean jumps.
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