Problem 6 · 2016 AMC 8
Easy
Arithmetic & Operations
careful-counting
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Answer: B — Median = 4.
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Hint 1 of 2
The median isn't an average here — it's the value sitting in the MIDDLE position once everything is lined up in order. With 19 names, which single position is the exact middle?
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Hint 2 of 2
A bar graph already has the data sorted by length, so just walk the bars left-to-right adding up their heights until your running total reaches that middle position — whatever bar you land on is the answer. You can stop the moment you pass it.
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Approach: locate the middle position by a running count of the bars
- With 19 values, the middle is the 10th one (9 below it, 9 above), so the median is whatever the 10th name's length is.
- Walk the bars in order and keep a running total: length 3 holds 7 names (covers positions 1–7); length 4 holds 3 names (covers positions 8, 9, 10).
- Position 10 falls inside the length-4 bar, so the median is 4.
- Why this transfers: for a median you never need to add the bars on the FAR side — just count inward until the running total reaches the middle position, then stop.
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