Question
Which of the following statements about the mean,
median, and mode is true when applied to a dataset with a skewed distribution?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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