Statistics extracts information by analysing variation in data
Variability is an important characteristic of most measurements that are made from people, including marks. There is variation between the individuals and also an element of randomness in most assessment activities. Variation is unavoidable and it is indeed this variation that provides us with information.
A major role of statistics is to display and describe this variation in ways that highlight the information in the data.
Even simple methods can show patterns that are not evident in the raw data. For example, sorting the values into increasing order can provide useful information.
A set of marks
The table below shows the marks from a maths test attempted by a class of 25 students.
81 | 72 | 98 | 34 | 54 |
43 | 73 | 91 | 52 | 48 |
71 | 89 | 81 | 54 | 72 |
39 | 46 | 72 | 85 | 90 |
75 | 40 | 33 | 69 | 84 |
What can you see?
Clearly, there is considerable variability between the students with the marks ranging from 34 to 98. But what else can be easily learned from the table?
Sorting the data can help
It is not easy to obtain further useful information from a table of raw data. Different displays of the data may however highlight meaningful patterns. Graphical displays are usually most effective, but even sorting the data into order gives some insight into the values.
The list below again shows the marks. Firstly, examine the unordered list of values. It is difficult to see any unusual features in the raw data.
Drag the slider to the right to sort the data into increasing order, then look for features in the sorted list of values.
Perhaps the two clusters correspond to boys and girls? Or groups of students who socialise together?
Even if the clusters do not correspond to other characteristics of the students, it may be worthwhile to separate out the lower cluster of students for additional tuition.