Mode (statistics)

In statistics, the mode is the value that has the largest number of observations, namely the most frequent value within a particular set of values. For example, the mode of {1, 3, 6, 6, 6, 7, 7, 12, 12, 17} is 6. The mode is not necessarily unique, unlike the arithmetic mean.

It is especially useful when the values or observations are not numeric since the mean and median may not be well defined. For example, the mode of {apple, apple, banana, orange, orange, orange, peach} is orange.

In a gaussian (i.e. bell curve) distribution, the mode is at the peak. The mode is therefore the value that is most representative of the distribution. For example, if you measure people's height or weight and the values form a bell curve distribution, the peak of this bell curve would be the most common height or weight among these people. The mean/average value can often be influenced by outliers or skews and can be well away from the peak of the distribution and therefore not a value representative of the largest number of people.

In gaussian distributions there is a mathematical relationship between the mean, median and mode known as Karl Pearson's empirical formula for the mode. This formula is that the mode is three times as far from the mean as the median is from the mean in the same direction. For example, the heights of physical education majors in a school might be distorted by the basketball team. Thus the average might be 6 foot, but the median would be less, at 5 ft 10 inches, and the mode would be at 5 ft 6 inches. Thus a quick check of whether the mean and median have similar values will tell if the distribution is skewed and provides a quick means of determining the value representative of the mode.