Measures of Center for AP Statistics (page 2)

By — McGraw-Hill Professional
Updated on Feb 5, 2011


Although the mean and median are both measures of center, the choice of which to use depends on the shape of the distribution. If the distribution is symmetric and mound shaped, the mean and median will be close. However, if the distribution has outliers or is strongly skewed, the median is probably the better choice to describe the center. This is because it is a resistant statistic, one whose numerical value is not dramatically affected by extreme values, while the mean is not resistant.

example: A group of five teachers in a small school have salaries of $32,700, $32,700, $38,500, $41,600, and $44,500. The mean and median salaries for these teachers are $38,160 and $38,500, respectively. Suppose the highest paid teacher gets sick, and the school superintendent volunteers to substitute for her. The superintendent's salary is $174,300. If you replace the $44,500 salary with the $174,300 one, the median doesn't change at all (it's still $38,500), but the new mean is $64,120—almost everybody is below average if, by "average," you mean mean. It's sort of like Lake Wobegon, where all of the children are expected to be above average.

example: For the graph given below, would you expect the mean or median to be larger? Why?


solution: You would expect the median to be larger than the mean. Because the graph is skewed to the left, and the mean is not resistant, you would expect the mean to be pulled to the left (in fact, the dataset from which this graph was drawn from has a mean of 5.4 and a median of 6, as expected, given the skewness).

Practice problems for these concepts can be found at:

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