The appropriate measure of center for a distribution is influenced by its shape. Here's a brief explanation of how different shapes dictate the best measure to use:
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Symmetrical Data: When a distribution is symmetrical (such as a normal distribution), the mean is the best measure of center because it accurately reflects the average value of the data. In symmetrical distributions, the mean, median, and mode are all generally located at the same point.
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Skewed Data: When a distribution is skewed, either to the left or right, the mean is affected by extreme values (outliers) and may not accurately represent the center of the data. In such cases, the median is preferred since it is less influenced by outliers and provides a better representation of the "typical" value in the dataset.
Therefore, the correct response is:
Symmetrical data means that the mean is the best measure of center.
In contrast, skewed data would require the median to be more representative of the center.