Measures of central tendency refer to ways to measure the central value of a distribution. Often, we call this the “average,” but in actuality, there are a number of ways you could measure an “average” value. The most common are mean (also known as the arithmetic mean), median, and mode. You’ve probably calculated these before without even realizing that they are statistical measures.

Mean

[latexpage]$\overline{X}=\dfrac{\sum X}{n}$

In order to compute the mean, first list the entire set of values (each value is referred to as X in the formula for mean.) Then, compute the sum of all the values. In the formula, this is the sum (∑) of all X values. Finally, divide the total by the number (n) of values.

For example, Fredericksburg, Virginia has the following average temperatures (in degrees Fahrenheit) in February over the past several years: 46.3, 38.6, 28.4, 35.5, and 37.4. What is Fredericksburg’s average mean temperature in February for this time period? First, add all the values together, which would be 186.2. Next, divide by the number of values. Here, we have five years of values, or five values, so we would divide by 5. 186.2 divided by 5 is 37.24. Thus, the mean temperature in Fredericksburg in February during this time period was 37.24 degrees.

Median

The median refers to the “middle” value, the point at which 50% of the values fall above it and 50% fall below it. Computing the median is simple: just list all of the values, in order, either from highest to lowest or from lowest to highest. Then, find the middle score. That’s the median.

What happens if there are two middle scores? Simply take the average. What if the two middle scores are the same? The median would be the same number as the two middle-most values.

For example, a given neighborhood has home values of \$50,500, \$89,900, \$110,000, \$126,500, \$200,000, and \$250,000. What is the median home value? Since there are six values, the middle-most values are \$110,000 and \$126,500. The average of these two values is \$118,250, which would be the median.

Mode

The mode is the most frequently occurring value. To compute the mode, list all of the values in the distribution as well as the frequency of each value (the number of times that value occurs in the dataset.) The value with the highest frequency is the mode.