Answer :
The pair of measures of center that indicates a positive skew in a normal distribution is when the mean is greater than the median. For the student's question, the correct choice is mean = 72, median = 66 (Choice C), which represents a positive skew.
The student's question pertains to the characteristic measure of center that indicates a positive skew in a normal distribution. In a positively skewed distribution, the mean is typically higher than the median, and both are higher than the mode. So, looking at the options provided, the pair of measures that indicates a positive skew would have a mean that is greater than the median, which in the provided choices is mean = 72, median = 66 (Choice C).
It's important to note that in a symmetrical distribution, the relationship among the mean, median, and mode is that they are all equal. However, when there is a skew, the mean is more significantly affected due to its mathematical nature, being the sum of all the data values divided by the total number of values. The mean is therefore pulled towards the extreme values in the distribution's tail, reflecting the skew more than the median or the mode.
