Which of the following statements is true?Group of answer choicesA. When the distribution is skewed to the left, mean > median > mode.B. When the distribution is skewed to the right, mean < median < mode.C. When the distribution is symmetric and unimodal, mean = median = mode.D. When the distribution is symmetric and bimodal, mean = median = mode.E. None of the above is correct.
Question
Which of the following statements is true?Group of answer choicesA. When the distribution is skewed to the left, mean > median > mode.B. When the distribution is skewed to the right, mean < median < mode.C. When the distribution is symmetric and unimodal, mean = median = mode.D. When the distribution is symmetric and bimodal, mean = median = mode.E. None of the above is correct.
Solution
The correct answer is C. When the distribution is symmetric and unimodal, mean = median = mode.
Here's why:
A. This statement is incorrect. When the distribution is skewed to the left (negatively skewed), the mean is less than the median, which is less than the mode (mean < median < mode).
B. This statement is incorrect. When the distribution is skewed to the right (positively skewed), the mean is greater than the median, which is greater than the mode (mean > median > mode).
C. This statement is correct. When the distribution is symmetric and unimodal (has one peak), the mean, median, and mode are all equal.
D. This statement is incorrect. When the distribution is symmetric and bimodal (has two peaks), the mean, median, and mode are not necessarily equal. The mean and median might be equal if the distribution is perfectly symmetric, but the mode will not be the same because there are two peaks.
E. Since C is the correct answer, this choice is incorrect.
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