The Mean and the Median

The most widely used measure of central value is the mean, x^-. The mean, also called the arithmetic mean or the average, is obtained by dividing the sum of replicate measurements by the number of measurements in the set:

where xi represents the individual values of x making up the set of N replicate measurements.  The median is the middle result when replicate data are arranged in increasing or decreasing order. There are equal numbers of results that are larger and smaller than the median. For an odd number of results, the median can be found by arranging the results in order and locating the middle result. For an even number, the average value of the middle pair is used as shown in Examplebelow. In ideal cases, the mean and median are identical. However, when the number of measurements in the set is small, the values often differ as shown in Example below.