Discussion
The arithmatic mean of 12 observations is 7.5. If the arithmatic mean of 7 of these observations is 6.5, then the mean of the remaining observations is
Answer: D
The mean of the remaining observations is 8.9.
\[ \begin{aligned} \text{total of 12} &= 12 \times 7.5 = 90 \\ \text{total of 7} &= 7 \times 6.5 = 45.5 \\ \text{mean of 5} &= \frac{90 - 45.5}{5} = 8.9 \end{aligned} \]
The remaining observations number \(12 - 7 = 5\); dividing by 7 instead would give about 6.4, which is not offered. 5.5, 8.5 and 9.2 do not come from the totals.
Working with totals rather than averages is the standard method for questions in which part of a group is removed.
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