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Which of the following pairs of measures of center indicates positive skew in a normal distribution?

A. mean = 66, median = 72
B. mean = 66, mode = 72
C. mean = 72, median = 66
D. mean = 72, mode = 66

Answer :

In a normal distribution, a higher mean than the median indicates positive skew. This is true for the pair where the mean is 72 and the median is 66. The correct option is C: mean = 72, median = 66.

In a normal distribution, if the mean is higher than the median, it indicates positive skew. This is because the mean is more affected by outliers and gets pulled towards the tail in a skewed distribution.

In a normal distribution, positive skew, also known as right skew, is indicated when the mean is greater than the median. This occurs because in a positively skewed distribution, the tail on the right side is longer and the mean is pulled in the direction of the tail. Among the given pairs, option C (mean = 72, median = 66) is the only one where the mean is greater than the median, signifying a positive skew in the distribution.

Additionally, the mean is the measure of center that tends to reflect skewing the most. In a perfectly symmetrical distribution, the mean, median, and mode are identical, but any skew will cause the mean to be pulled toward the tail. Therefore The correct option is C: mean = 72, median = 66.

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