Expansion dimensions, also called measures of variation, are measures that help us to identify the extent or variation of a data set.
At this point you may not fully understand what we mean by dispersion or variation. We will illustrate it with an example.
For example, suppose “Professor Johnson” teaches calculus 1 and “Professor Peter” also teaches calculus 1.
After some research, it was found that:
The grades of 6 randomly selected students attending Johnson’s class are typically
100 10 70 90 40 90
The grades of 6 randomly selected students attending Peter’s class are in general
70 60 70 65 60 75
Plot the notes on a number line as shown in the picture above. Looking at the number line, what can you conclude about the classes?
What else can we conclude from the graph?
The performance of the students in Peter’s class is almost the same.
Since the grades are close together, we say the grades are in Peter’s class low scatter or a small amount of variation.
However, the grades in Johnson’s class are further apart. Therefore, the degree of dispersion is greater.
How big is the spread or variation?
We can use the range to find it.
The range is the easiest measure to calculate for the dispersion.
To find it, use the formula below
Range = highest value – lowest value
The range for Johnson’s class is 100-10 = 90
The range for Peter’s class is 75-60 = 15
Perhaps you can even draw conclusions about the teaching style of the professors or the behavior of the students in the classroom.
If we were to try to blame Professor Johnson, you might draw the following conclusions.
Perhaps Professor Johnson is not trying to help everyone in the class.
Perhaps his teaching style doesn’t work for everyone.
The grades for Peter’s class are not great. However, it is possible that what the students get will all get pretty much at the same time.
Since the range is strongly influenced by extreme values, it is not a very reliable measure of the variation.
In the next lesson, you will learn about standard deviation, which is the most important and probably the most accurate measure of dispersion.