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If a distribution is skewed left, which of the following is true of the data set?

A. The mean is greater than the median.
B. The mean and the median are equal.
C. The mean is less than the median.
D. The mean is the best measure of center.

1 Answer

5 votes

Final answer:

The mean is less than the median in a distribution that is skewed left, making option C correct, since the mean is influenced more by the extreme lower values present in the left tail of the distribution.

Step-by-step explanation:

If a distribution is skewed left, this suggests that the data values are spread out more to the left of the central tendency, creating a long tail on the left side of the distribution graph. When a distribution is skewed left, the majority of the data values, including the median, are located to the right of the mean, which gets pulled in the direction of the longer, thinner tail.

Therefore, the correct answer to the question is C. The mean is less than the median. Additionally, in a left-skewed distribution, the mean is not the best measure of center, as it is affected more by the extreme lower values on the left tail of the distribution. Rather, the median often provides a better central value for skewed distributions as it is not as influenced by the extreme values as the mean is.

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