Mean, median and mode
To summarise numerical variables, there are three measures that are commonly used: mean, median and mode. To explain how to proceed with these measures, let's look at some examples.
The mean is the average of a series of measurements or scores. To calculate the mean, you add up all the individual measurements or scores and then divide this total by how many scores there are (it is the sum divided by the number of individual values). Although the mean is the most commonly used of the measures mentioned here, the median or the mode may sometimes be more appropriate. The median is a measure of central location, where half of the measures are below and the other half are above this value. The mode is the most common result (the most frequent value) of a test, survey or experiment.
For example, imagine a school exam taken by 10 students with possible scores from 0 to 100. Nine students score 95 but one person scores 5. The mean is calculated by adding up the total scores (9 × 95 + 5 = 860) and dividing by the number of scores (10), which gives a mean of 86. That one person with the low score really throws off the final statistic! The median, however, is 95 and in this case is a better description of how most people did in the exam. The mode would be the most common score which would also be 95 in this example. In this case the median or mode might be more useful than the mean.
Seven farmers in your community keep goats. You record how many goats each farmer has and the results are 8, 1, 3, 7, 1, 6 and 9. What is the mean number of goats owned by these farmers and what is the median number?
The mean is 5. It is the sum of the scores (35) divided by the number of farmers (7). If you put the numbers in order they are 1, 1, 3, 6, 7, 8, and 9. The middle value is 6 and therefore the median is 6.
Note the difference in the values between the mean and median. The mean or average can be influenced by extreme or outlying values at either end of the scale, but the median is not. If the number of values is even, there isn't a middle value, so to calculate the median you take the mean of the two middle numbers.
For example, if there were only six farmers and the number of goats they owned were 10, 12, 14, 16, 18 and 20, the two middle numbers are 14 and 16, so the median is 14+16 divided by 2, which equals 15.
Supposing the numbers of goats owned by the seven farmers are 3, 4, 7, 7, 7, 9 and 10. What is the mode of the numbers of goats?
Looking at these scores, you can see that 7 is the most common number of goats because three farmers have 7 goats. The mode of the numbers (also referred to as the modal number) of goats is therefore 7.
Sometimes it is more appropriate to think about the modal number since this represents the most common situation.