Comparing distributions

Complete the following table. The data shows the scores in an English and Maths test for a set of ten students.

If you were to compare the scores in the two subjects, which measure of average would you use and why?

Range

The range of scores in English ( {37}) is far greater than the range of scores in the Maths ( {4}). However, the range is not an average, but a measure of the spread of the values (or marks in this case).

Mean

The mean score in each subject is {78} - which implies that the scores of the students are similiar in English and Maths. But looking at the actual scores, you can see that this is not the case. However, for the mean scores to be the same, the total of the scores of the ten pupils in both English and Maths would have to be the same.

Median

If you compare the medians ( {71} and {78}), you might assume that the students generally scored less well in English. This is partly true, but there are also some much higher scores. The median is only a measure of the middle value, as there will be the same number of values above and below this middle value.

Mode

If you just state the modal score for each subject ( {101} and {78}), you have no information about the scores of the other students.

So, which is best?

It depends on the context in which the result is to be used.

The mean is usually the best measure of the average, as it takes into account all of the data values.

However, in order to highlight the differences in the marks scored and to give maximum information, a combination of the median and the range would be best.

In summary, both English and Maths have a mean score of {78}, however English has a median score of {71} and a range of {37}, and Maths has a median score of {78} and a range of {4}.