Median

The median is a measure of central tendency and is the point in a group of values with an equal number of values above and below that point.

The computation of the median is as follows.

• For an odd number of values, the position of the median is given by (N + 1)/2. If we have 15 cases, the median is the 8th case.
• For an even number of cases (N + 1)/2 does not give a whole number. In this case, the median is the (arithmetic) mean of the two values immediately above and below.

For example, the data set in Table 1 consists of 11 test scores.

First of all, the values need to be sorted from smallest to largest value: 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9. Then, the midpoint needs to be found that splits the sample into two halves. In this example we have an odd number of participants, so we will have a midpoint that represents the point on which an equal number of values on each side is present. To the left of the midpoint, the values 4, 5, 6, 6, and 6 are present, and to the right, the values 7, 7, 8, 8, and 9. In this example, the midpoint of the row of numbers has a value of 7, so the median is 7.

Consider also a sample of an even number of participants who have achieved the test scores 4, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, and 9. The midpoint has to be computed by finding the two values in the middle—here, 6 and 7—and the mean of the two will be the median, so the median is 6.5.