For a negatively skewed, unimodal distribution, which of the following relationships holds?
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A. B. C. D.C
In a negatively skewed distribution, very low values are more common than correspondingly large values. This skews the distribution to the left, moving the mean to the left of the median.
In a negatively skewed, unimodal distribution, the tail of the distribution is longer on the left side and the majority of the data points are concentrated on the right side. This means that the distribution is "skewed" towards the left.
Let's analyze each answer choice:
A. mode < median: The mode is the value that appears most frequently in the distribution, while the median is the middle value when the data is arranged in ascending or descending order. In a negatively skewed distribution, the tail is longer on the left, so the mode is likely to be located towards the right side where the majority of the data points are concentrated. Therefore, it is not necessarily true that the mode is less than the median. This relationship does not hold for a negatively skewed, unimodal distribution.
B. mean > median: The mean is the arithmetic average of all the data points, while the median is the middle value. In a negatively skewed distribution, the tail is longer on the left, which means that the left tail pulls the mean towards the left, making it lower than the median. Therefore, this relationship holds for a negatively skewed, unimodal distribution.
C. mean < median: As explained in the previous answer choice, the mean is pulled towards the left by the longer left tail in a negatively skewed distribution, making it lower than the median. Therefore, this relationship holds for a negatively skewed, unimodal distribution.
D. mean > mode: The mean is the average of all the data points, while the mode is the value that appears most frequently. In a negatively skewed distribution, the tail is longer on the left, so the mode is likely to be located towards the right side where the majority of the data points are concentrated. Therefore, it is not necessarily true that the mean is greater than the mode. This relationship does not hold for a negatively skewed, unimodal distribution.
Based on the explanations above, the correct answer is either B. mean > median or C. mean < median. Both options describe the relationship that holds true for a negatively skewed, unimodal distribution.