Mean and median are measures of central tendency in a data set. Mean is the average of all values, while median is the middle value in a sorted list. The best method depends on the data. Mode is the most common value. Mean can be skewed by outliers, while median is more typical. All three methods can be used in data analysis.
In statistics, mean and median are different measures of central tendency in a data set, or the tendency of numbers to cluster around a particular value. In a group of values, it may be desirable to find the most typical one. One way to do this is to find the mean, or average, which is the sum of all values divided by the total number of values. Another way is to find the median, or mean value, which is the one in the center of a sorted list of numbers. The best method to use depends on the application and the nature of the data.
Mean
Getting the mean of something is equivalent to getting the mean number in a data set. The sum of the values in the collection 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 get a sum of 415, which is divided by 5 to get the average score of 83. After calculating this, the teacher can assign a grade to the student.
Medium
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 in the set. This varies slightly from the average of 83. A teacher may want to look at an average score, as they tend to rule out an unusually low score, such as 60, which would lower the average.
Where the number of values is even, an average of the two middle numbers is taken. These two numbers are added and divided by two. For example, in a class of ten students the scores on a test might be, in ascending order, 48, 56, 57, 61, 65, 68, 68, 71, 77, and 82. The median for this dataset would be the average of the fifth and sixth numbers, 65 and 68, which is 66.5.
Applications
These methods are both used to find a “typical” value from a set of data. The mean is the most commonly used measure of central tendency, but there are cases where it is not appropriate. For example, the data may be ‘skewed’, meaning that most numbers are towards the lower or higher end of the scale, or that there is one value that is very different from all the others – this is known as a outlier. Especially in a small dataset, the average value in these cases will not be typical.
For example, if five students take a test and the scores are 24, 85, 89, 91, and 95, the average score is 60.6. This, however, is not typical: the average was reduced by a marginal score of 24, probably because one student hadn’t studied. In this case, the median of 89 is much more typical.
Another occasionally used method is mode, which is simply the most common value in a dataset. It is sometimes used when the possible values in a dataset are limited and mutually exclusive. For example, a survey of laptop owners could be conducted to find the most popular brand. In this case, an average or middle brand would be meaningless and the most popular brand would be Fashion.
As an example where all three methods could be used, some data about the employees of a company could be collected. An analysis might calculate the average salary, but this can be skewed by a small number of very high-ranking employees in upper management, so the average salary might give a better idea of what a typical employee is being paid. If the data is broken down by educational qualifications, it could be found that the majority of employees have a university degree: this would be the method.
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