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    Question

    If a dataset has a mean significantly higher than the

    median, which of the following is most likely true?
    A The dataset is normally distributed. Correct Answer Incorrect Answer
    B The dataset is positively skewed Correct Answer Incorrect Answer
    C The dataset is negatively skewed Correct Answer Incorrect Answer
    D The dataset has no outliers. Correct Answer Incorrect Answer
    E The mode will always be lower than the mean. Correct Answer Incorrect Answer

    Solution

    In a positively skewed distribution, the tail extends to the right, pulling the mean higher than the median. This occurs because extreme high values disproportionately influence the mean compared to the median, which is less sensitive to outliers. For example, income data often exhibits positive skewness because a few individuals earn much more than the majority. Understanding skewness helps in choosing the right statistical methods for analysis, as normality assumptions might not hold. Why Other Options Are Wrong : A) Normally distributed data has the mean and median roughly equal. C) Negative skewness occurs when the tail extends to the left, causing the median to exceed the mean. D) Outliers often cause skewness; their absence suggests symmetry. E) The mode can vary and isn’t always lower than the mean in skewed data.

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