Discussion
State which of the following statements is true ?
Answer: A
The true statement is that the arithmetic mean is proper representative of the group if the standard deviation is smaller.
The standard deviation measures how far the observations are scattered around the mean. A small standard deviation means the values are close together, so the mean is typical of them; a large one means the values are spread widely, and the mean may be far from most of them.
So the mean is a poorer representative when the standard deviation is larger, and its representativeness does depend on dispersion. The size of the standard deviation says nothing about the size of the mean itself: two groups can have the same mean and very different spreads.
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