What is the Difference Between Median and Mean?

In statistics, mean and median are different measures of the central tendency in a set of data, or the tendency of the numbers to bunch around a particular value. In a group of values, it might be desirable to find the one that is most typical. One way of doing this is to find the mean, or average, which is the sum of all the values divided by the total number of values. Another way is to find the median, or middle, value, which is the one in the center of an ordered list of numbers. The better method to use depends on the application and on the nature of the data.

Getting the mean of something is the same as obtaining the average number in a data set. The sum of the values in the set is divided by the number of values. For example, a teacher might evaluate five test scores, all weighted equally, to determine a grade for a student. If the five test scores are 80, 85, 60, 90, and 100, these numbers are added together to give a sum of 415, which is divided by 5 to get the mean score of 83. After calculating this, the teacher can assign a grade to the student.

In a median measurement, the data are arranged from lowest to highest: 60, 80, 85, 90 and 100. The middle number in this set is the median. In this example, the median is 85, the third, and middle, number of the set. This varies slightly from the mean of 83. A teacher may wish to look at a median score, as it tends to rule out an unusually low score, like 60, that would lower the average.

Where the number of values is even, an average of the two central numbers is taken. These two numbers are added together and divided by two. For example, in a class of ten students the scores in a test might be, in ascending order, 48, 56, 57, 61, 65, 68, 68, 71, 77 and 82. The median for this data set would be the average of the fifth and sixth numbers, 65 and 68, which is 66.5.

These methods are both used to find a “typical” value from a set of data. The mean is the most commonly used measurement of central tendency, but there are cases where it is not appropriate. For example, the data may be “skewed,” meaning that most of the numbers are toward either the low or the high end of the scale, or that there is one value that is wildly different from all the others — this is known as an outlier. Especially in a small set of data, the average value in these cases will not be typical.

For example, if five students sit a test, and the scores are 24, 85, 89, 91 and 95, the mean score is 60.6. This, however, is untypical — the average has been dragged down by one outlying score of 24, possibly because one student had not been studying. In this case, the median of 89 is much more typical.

Another method occasionally used is the mode, which is simply the most common value in a data set. It is sometimes used where the possible values in a set of data are limited and mutually exclusive. For example, a survey of laptop computer owners might be carried out to find the most popular brand. In this case, a mean or median brand would not make sense, and the most popular brand would be the mode.

To give an example where all three methods might be used, some data relating to employees of a company might be collected. An analysis might calculate the average salary, but this may be skewed by a small number of very high earners in senior management, so the median salary might give a better idea of how much a typical employee is paid. If the data is broken down by educational qualifications, it might be found that the majority of employees have a university degree — this would be the mode.