For a variable X (representing a sample or a population), let us define the median of X as the value that divides the observations on X into two equal parts; it is a positional value—half of the observations on X lie below the median, and half lie above the median. Since there is no standard notation in statistics for the median, we shall invent our own: the population median will be denoted as “Med;” the sample median will appear as “med.”
Since the median is not a calculated value (as was the mean) but only a positional value that locates the middle of our data set, we need some rules for determining the median. To this end, we have rules for finding the median:
Note that for either case 2a or 2b, the median is the term that occupies the position (or ) in the increasing sequence of data values.
Given the variable X: 8, 7, 12, 8, 6, 2, 4, 3, 5, 11, 10, locate the median. Arranging the observations in an increasing sequence yields 2, 3, 4, 5, 6, 7, ...