Median
The median is the middle score in a distribution of scores that have been ranked in numerical order. If the median is located between two scores, it is assigned the value of the midpoint between them. For example, the median of 23, 34, 55, and 68 would equal 44.5 (that is, (34 + 55)/2). The median is the best measure of central tendency for skewed distributions, because it is relatively unaffected by extreme scores. Note that in the example below the median is the same in both sets of exam scores, even though the second set contains an extreme score. The means for the data sets differ however, due to the one extreme score on Exam B.
Exam A: 23, 25, 63, 64, 67
Exam B: 23, 25, 63, 64, 98
When Disraeli pointed out the ease of lying with statistics, he might have been referring, in particular, to measures of central tendency. Suppose a baseball general manager is negotiating with an agent about a salary for a baseball catcher of average ability. Both might use a measure of central tendency to prove their own points, perhaps based on the salaries of the top seven catchers, as shown below. The general manager might claim that a salary of $340,000 (the median) would provide the player with what he deserves, based on an average salary of the other players. The agent might counter that a salary of $900,000 (the mean) would provide the player with what he deserves, based on an average salary of the other players. Note that neither would technically be lying--they would simply be using statistics that favored their position. As Scottish writer Andrew Lang (1844-1912) warned, beware of anyone who "uses statistics as a drunken man uses lampposts--for support rather than for illumination."
Salaries of Top 7 Major League Baseball Catchers
225,000
250,000
275,000
340,000
400,000
475,000
4,335,000
Learning Check #7:
What is the median number of brothers and sisters listed in Learning Check #5?
Learning Check #8:
Note that the mean number of brothers and sisters is quite a bit different than the median number of brothers and sisters. In this case, which measure of central tendency would be most appropriate to report? Why?