Multiple choice

The mean of five observations x, x + 2, x + 4, x + 6, x + 8 is m. What is the mean of the first three observations?

  1. m

  2. m - 1

  3. m - 2

  4. m - 3
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C Correct answer
Explanation

The mean of x, x+2, x+4, x+6, x+8 is (5x + 20)/5 = x + 4 = m. Thus, x = m - 4. The first three observations are x, x+2, x+4. Their mean is (3x + 6)/3 = x + 2. Substituting x = m - 4, we get (m - 4) + 2 = m - 2.

AI explanation

The mean of the five observations is m, which equals (x + x + 2 + x + 4 + x + 6 + x + 8) divided by 5, simplifying to x + 4. The mean of the first three observations is (x + x + 2 + x + 4) divided by 3, which equals x + 2. Substituting m for x + 4, the mean of the first three observations becomes m - 2.

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