Measures of Central Tendency

    There are three common measures of the center of a distribution: mode, median and mean.
  • The mode

    The mode is the most frequent score in a set of measures. Some distributions have no mode, e.g., 123, 154, 167, 132.

    The mode is very unstable--minor fluctuations in the data can change it substantially; for this reason it is seldom calculated. Its principal use is colloquial: "The distribution of X is 'bimodal.'"

  • The median
    The median is the middle score in the distribution. In a distribution where N is an odd number the median is the middlemost score: for 32, 35, 36, 43, 74, the median is 36. By convention, the median of the distribution where N is an even number the median is the mean of the two middlemost scores: for 123, 154, 160, 187 is taken to be half way between the two center values: Median = (154 + 160)/2 = 157.
  • The mean
    The mean (average, or arithmetic mean) is the sum of the scores in the distribution divided by the number of such scores. The mean of 12, 13, 23, 43, 32 is

    Mean = (12 + 13 + 23 + 43 + 32)/5 = 24.6

Properties of Mean and Median

The most important property of the mean and median is embodied in a simple example. Observe what happens to a set of five scores when the largest one is increased by several points:

Set A: 12, 13, 23, 32, 43
Mean = 24.6 Median = 23

Set A Altered: 12, 13, 23, 32, 143
Mean= 44.6 Median = 23

That is, the mean is influenced by outliers whereas the median is not.

And another thing....

One thing I always found curious is that Mean, Median and Mode, as well as Middle, Meridian, Middling, Mediocre all begin with the letter "M", which is in the middle of the alphabet! That's some freaky stuff. Also, the words, No, Not, Never, Nowhere, Negative, Nobody, all begin with the letter "N", which is not in the middle of the alphabet.