The best answer to the question regarding how the shape of a distribution determines the appropriate measure of center is:
C: Symmetrical data means that the mean is the best measure of center.
Here's the reasoning:
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Symmetrical distributions: When data is symmetrically distributed (like in a normal distribution), the mean, median, and mode are all located at the same central point. Therefore, the mean is a very good measure of central tendency because it accurately reflects the center of the distribution.
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Skewed distributions: In contrast, when a distribution is skewed (either left or right), the mean is affected by extreme values (outliers), pulling it away from the center of the bulk of the data. In these cases, the median is typically considered a better measure of center, as it is less influenced by extreme values.
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Option A is partially correct but too vague. While additional information can refine our selection of measures, typically the basic shape helps indicate the best choice.
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Option B is inaccurate; skewed data generally suggests that the mean is not the best choice for a measure of center, and the median is preferred instead.
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Option D is incorrect because the shape of the distribution significantly influences which measure of center is appropriate.
Therefore, understanding the shape of the distribution is crucial in determining whether to use the mean or the median as the most representative measure of center.