Multiple choice

If the mean of the observations: x,x+3,x+5,x+7,x+10 is 9 the mean of the last three observations is

  1. $\displaystyle 12\frac{1}{3}$
  2. $\displaystyle 12\frac{2}{3}$
  3. $\displaystyle 11\frac{1}{3}$
  4. $\displaystyle 13\frac{2}{3}$
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C Correct answer
Explanation

The mean of x, x+3, x+5, x+7, x+10 is (5x + 25) / 5 = x + 5. Given x + 5 = 9, we find x = 4. The last three observations are x+5, x+7, x+10, which are 9, 11, 14. Their mean is (9 + 11 + 14) / 3 = 34 / 3 = 11 1/3.

AI explanation

The mean of the five observations is (x + x + 3 + x + 5 + x + 7 + x + 10) divided by 5, which simplifies to (5x + 25) divided by 5, equaling x + 5. Setting this equal to 9 gives x = 4. The last three observations are x + 5, x + 7 and x + 10, which become 9, 11 and 14 when x = 4. Their mean is (9 + 11 + 14) divided by 3, equaling 34 divided by 3, or 11 and 1/3.

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