Discussion
For a certain Normal distribution, the first moment about 10 is 40. What is the arithmetic mean ?
Answer: C
The arithmetic mean is 50.
The first moment about a point A is the mean of the deviations from A:
\[ \begin{aligned} \mu_{1}' &= \frac{\sum (x - A)}{n} = \bar{x} - A \\ 40 &= \bar{x} - 10 \\ \bar{x} &= 50 \end{aligned} \]
This holds for any distribution, normal or not. 40 forgets to add back the point about which the moment was taken. 30 subtracts 10 instead of adding it, and 20 has no basis in the data. As a check, the first moment about the mean itself is always zero.
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