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    Question

    Which of the following statements about the mean,

    median, and mode is true when applied to a dataset with a skewed distribution?
    A The mean, median, and mode are all equal in a negatively skewed distribution. Correct Answer Incorrect Answer
    B The mean will always be less than the median in a positively skewed distribution. Correct Answer Incorrect Answer
    C The mode is the most reliable measure of central tendency in a skewed distribution. Correct Answer Incorrect Answer
    D The median is less influenced by outliers than the mean. Correct Answer Incorrect Answer
    E The mode will always be greater than the median in a skewed distribution. Correct Answer Incorrect Answer

    Solution

    In a skewed distribution, the mean is heavily influenced by outliers or extreme values. For example, in a positively skewed distribution (right-skewed), where the tail is extended to the right, the mean will be greater than the median because the extreme high values push the mean to the right. The median, however, represents the middle value and is less affected by the extreme values, making it a more reliable measure of central tendency in skewed data. Therefore, the median is often preferred in the presence of outliers and skewness. The mode, while useful in some cases, does not always represent the center in skewed data and can sometimes be non-representative. Why Other Options Are Incorrect: • A: The mean, median, and mode are not equal in a skewed distribution. This occurs only in symmetric distributions like the normal distribution. • B: In a positively skewed distribution, the mean is greater than the median, not less. • C: While the mode represents the most frequent value, it is not always the most reliable measure of central tendency, particularly in skewed distributions. • E: The mode does not necessarily have to be greater than the median in skewed distributions.

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