The 1-Var Stats procedure, described in the previous Calculator Tip box, will, if you scroll down to
the second screen of output, give you the median (as part of the entire five-number summary of the data:
minimum, lower quartile; median, upper quartile; maximum).
Resistant
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 .
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).Measures of Spread
Simply knowing about the center of a distribution doesn’t tell you all you might want to know about the
distribution. One group of 20 people earning $20,000 each will have the same mean and median as a
group of 20 where 10 people earn $10,000 and 10 people earn $30,000. These two sets of 20 numbers
differ not in terms of their center but in terms of their spread, or variability. Just as there are measures of
center based on the mean and the median, we also have measures of spread based on the mean and the
median.