Measures of Central Tendency

An important concept in statistics is that of central tendency. A measure of central tendency aims to summarize data with a single value that captures what is typical about the data.

There are three measures of central tendency: the mean, the median, and the mode:

• The mean is the average value. There are a few different types of means. The three most common are:
  • The arithmetic mean is the most commonly-used of the means and is often what is meant when by simply "mean." The word "average" also typically refers to the arithmetic mean. The arithmetic mean is calculated by adding the values of each observation and dividing by the number of observations.
  • The geometric mean is calculated by multiplying the values of each observation and then taking the n^th root, where n is the number of observations.
  • The harmonic mean is calculated by adding the reciprocals of each observation, dividing by the number of observations, and taking the reciprocal of that.
• The median is numerically the middle value in a data set. Half of the observations are above the median and half are below (if there are an even number of observations in a data set, the median is the arithmetic mean of the two middle observations).
• The mode is the most common value in the data set. A data set may have more than one mode.