Problem 19 · 1995 AJHSME
Hard
Arithmetic & Operations
medianread-graph
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Answer: D — 4.
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Hint 1 of 2
Median is the MIDDLE value, not the tallest bar. Read carefully: the bar HEIGHT is how many families, and the number you're averaging over is the children-per-family on the bottom axis. First find how many families there are in all.
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Hint 2 of 2
Once you know the total count, the median sits at the middle position. You don't need to write every value — just walk along the bars counting until you reach that middle spot.
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Approach: total the families, then walk the bars to the middle position
- Read the bars as counts of families: 2 families have 1 child, 1 has 2, 2 have 3, 2 have 4, 6 have 5 — that's 2 + 1 + 2 + 2 + 6 = 13 families.
- With 13 values in order, the median is the 7th one (six below it, six above). Walk the bars: positions 1–2 are '1 child,' position 3 is '2,' positions 4–5 are '3,' positions 6–7 are '4.' The 7th lands in the '4 children' group.
- So the median is 4.
- The trap this catches: the '5 children' bar is tallest, so it's tempting to answer 5 — but tallest is the MODE, not the median. Median = middle position. Sanity check: the 7th value is 4, comfortably below the popular 5's that pile up at the top end.
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