Problem 4 · 2011 AMC 8
Easy
Arithmetic & Operations
mean-median-mode
Here is a list of the numbers of fish that Tyler caught in nine outings last summer: 2, 0, 1, 3, 0, 3, 3, 1, 2. Which statement about the mean, median, and mode is true?
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Answer: C — mean < median < mode.
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Hint 1 of 2
Sorting the list does all three jobs at once: it puts the middle value (median) in plain sight, makes the repeated value (mode) easy to spot, and the mean is just the total split 9 ways.
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Hint 2 of 2
Mode = the value that appears most, median = the middle one (the 5th of 9), mean = sum ÷ 9 — three different ways to say "a typical value."
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Approach: sort once, then read off all three
- Sorted: 0, 0, 1, 1, 2, 2, 3, 3, 3.
- Mode = 3 (it shows up three times). Median = the 5th value = 2. Mean = 15/9 = 5/3 ≈ 1.67.
- So 5/3 < 2 < 3 ⇒ mean < median < mode.
- Intuition: the two zero-fish days drag the mean down below the middle value, which is why the mean ends up smallest here.
Mark:
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