🇺🇸 AMC 8 ⇄ switch contest
2010 AMC 8

Problem 4

Problem 4 · 2010 AMC 8 Easy
Arithmetic & Operations mean-median-mode

What is the sum of the mean, median, and mode of the numbers 2, 3, 0, 3, 1, 4, 0, 3?

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Answer: C — 7.5.
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Hint 1 of 2
Sorting the list once does double duty: it lines up the middle for the median and stacks the repeats so the mode jumps out. Do that single step before anything else.
Still stuck? Show hint 2 →
Hint 2 of 2
Mean / median / mode each answer a different question — the fair share, the middle, the most popular. Sort first, then read two of them straight off the list.
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Approach: sort once, then read off median and mode
  1. Sort: 0, 0, 1, 2, 3, 3, 3, 4. Now everything is easy to see.
  2. Mode (most repeated) = 3, sitting in an obvious cluster. Median (middle): with 8 numbers, average the 4th and 5th: (2 + 3)/2 = 2.5.
  3. Mean (fair share): sum = 16, so 16/8 = 2.
  4. Total: 3 + 2.5 + 2 = 7.5.
  5. Why this transfers: the three M's are easy to mix up. Naming what each one does — popular, middle, fair-share — keeps you from grabbing the wrong one under time pressure.
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