There are lots of ways to be average

When researchers talk about average, they use the term “Central Tendency”. In other words, where does the center of a set of numbers tend to be. When officials report the average salary in the United States, it could be one of three measures of central tendency: mean, mode, or median.

Most people think of the arithmetic mean (which we will refer to as the mean) as the average. The mean for a set of numbers is calculated by summing all of the numbers in the set and dividing that total by the number of numbers in the set. If we were considering the numbers 1, 5, 2, 3, 5, 4, 5, and 7, the mean would be 4 . (1 + 5 + 2 + 3 + 5 + 4 + 5 + 7 = 32.  Since there are 8 numbers in the set, we divide 32  by 8 and get  4 as the mean). The mean is commonly used in statistical formulas. One problem with the mean is that is very sensitive to extreme scores, particularly with small samples. For example, the mean for 1, 1, 1, 2, 2, and 1000 would be very high (167.83) and might not be the best  representation of the average for that set of numbers. Excel can be used to calculate means and standard deviations.

The mode is another way to describe the center. The mode is the number that occurs most often. In the numbers  1, 5, 2, 3, 5, 4, 5, and 7, the mode is 5 because 5 occurs three times. No other number occurs three times in the set. It is possible to have more than one mode. If there had been three 2s, then 5 and 2 would have been the mode. In that situation, we say that our distribution is bimodal (two modes). It is easy to remember that the mode is the most frequent number because mode and most sound very similar.

A third measure of central tendency is the median. When the numbers are put in order from lowest to highest, the median is the number directly in the center. When we order the set of numbers  1, 5, 2, 3, 5, 4, 5, and 7, they are 1, 2, 3, 4, 5, 5, 5, and 7. Because we have eight numbers, there is no middle number. The middle falls between the 4 and the 5. The median therefore is 4.5 (the average of 4 and 5). Remembering that the median is the middle is easy, since the median is the middle of the highway. Regardless of how skewed the numbers are in our distribution, we know that half of the scores are above the median and half of the scores are below it. This may not be the case with the mean and the mode. The federal government often uses the median to report the average income in United States.

Del Siegle, Ph.D.
Neag School of Education – University of Connecticut