Measures of Central Tendency

The mean is a good measure of central tendency because its score changes as the values below and above it change. For example, in the example where we changed all the scores below the median to 40 out of 100 (the numbers in blue in the table above) this had no effect on the median score. However, when using the mean, the representation of the group of data is much more accurate. Indeed, if we calculate the mean for the original data and compare it with the data where we changed all the scores below the median to 40, the sum of all the score changes from 5875 to 5596 and the mean score changes from 58.75 to 55.96 out of 100. Clearly, if our tutor wanted to understand the overall performance of the 100 students, a difference of 2.79 marks in the mean score matters.

As a result, the mean is much more effective at measuring the central position in a frequency distribution because it takes into account not only the total number of scores but also their distance from the central position. The advantages of this can be seen further when we examine tests for normality and the use of the mean in other statistical tests.