What is the relationship among the mean, median and mode in a symmetric distribution?
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A. B. C. D. E.Explanation
Since the distribution is symmetric, all three are equal.
In a symmetric distribution, the mean, median, and mode are related in a specific way. Let's examine each answer choice to determine the correct relationship:
A. Mean is always the smallest value: This statement is incorrect. The mean is not necessarily the smallest value in a symmetric distribution.
B. Mean is always the largest value: This statement is also incorrect. The mean is not necessarily the largest value in a symmetric distribution.
C. None of these answers: This answer choice suggests that none of the statements provided in the previous answer choices are correct. However, we still need to evaluate the remaining answer choices to determine the correct relationship.
D. Mode is the largest value: This statement is incorrect as well. In a symmetric distribution, the mode represents the value or values that occur most frequently, and it is not necessarily the largest value.
E. All equal: This answer choice suggests that the mean, median, and mode are all equal in a symmetric distribution. This is the correct relationship. In a symmetric distribution, where the data is evenly distributed around the center, the mean, median, and mode are all equal.
Therefore, the correct answer is E: All equal.