ExplanationCalculating Measures of Central Tendency
Level 1 showed how the three different measures of central tendency are each suited to different types of data. We will now see how the different measures can give different results depending on the pattern of values in your data. We will also show you how to calculate the values of the three different measures.
Now we know how to calculate the values, we can see how each different measure performs with different patterns of data.
- The mode is calculated by counting how often each value occurs. There is no formula, you just count the values and see which one occurs most often. That value is the mode;
- The median is found by first sorting your data in order and then finding the middle value. If you have an even number of data points, there won't be a value right in the middle, so you take the two middle values, add them together and divide the answer by 2;
- The mean is calculated using a formula which adds all the values together and then divides by the number of values there are.
- The mean is badly affected by extreme values. Imagine you had the data: 1,2,3,4,400. The mean is 410/5 = 82, which doesn't really reflect where any of the data lies
- The mode can be misleading if several values all appear equally often. It is useless if all the values in your data are different, as they each appear once only!
- The median can smooth out extreme values but can produce the least frequently occurring value, as in this example: 1,1,1,2,3,3,3
Reporting Your Findings
Once you have calculated your measures of central tendency, you usually want to report them. The best way to do this is in a table.