Is A Median More Accurate Than A Mean?

The median and the mean are ways used in mathematics to express the central tendency of a group of numbers or values. Laerd statistics describe a central tendency as "a single value that attempts to describe a set of data by identifying the central position within that set of data."

The mean — or average — can be used to measure the central tendencies of a group of values. These values can be discrete or continuous but the mean is more often used in groups of continuous data. The mean is derived by adding all the values together and dividing this total by the number of values added together. For example, the mean of 6, 2 and 9 would be (6+2+9) divided by 3, equaling 5.67.

In order to calculate the median value of a group of numbers, the group must first be arranged in ascending order of magnitude. The middle value of the ascending numbers is the median value. In the example of 6, 2 and 9, arrange the numbers into an ascending order of magnitude, so this list would become 2, 6 and 9. There are three values so the middle value is 6; 6 is the median. If the number of values in the list is even — i.e. there is no middle value — then add the values either side of the halfway point and divide the total by two to derive the median.

The mean is the most accurate way of deriving the central tendencies of a group of values, not only because it gives a more precise value as an answer, but also because it takes into account every value in the list. For example, a group of five school children are taking part in a long jump competition; two of the children jump 1 foot, one jumps 2 feet, one jumps 4 feet and one jumps 8 feet. The values, in ascending order, are 1, 1, 2, 4 and 8, giving a median of 2 feet. The mean of the group of values is 3.2 feet. However, if the child who leapt 8 feet had in fact pulled off a jump of 16 feet, then the median would not change to accommodate this, whereas the mean would rise to 4.8 feet in response to the higher value. The median is more suited to discounting high or low results that are suspected to be anomalous.