Measures of Variance
In a previous chapter, we learn to summarize a set of numbers into a single number that we call the mean, median, mode, i.e., the central location. But often, knowing the central location is not enough, because 2 sets of numbers can have identical mean, but look very much different.
To illustrate this, image 2 people. Call them Sunita and Sanjay. They are good friends, go to the same school, take the same 5 courses. At the end of the semester, they have identical mean of 81, identical median of 80, and identical mode of 80. But are they equally good students? Let us look at their transcripts.
| Name | Homework | Term Test#1 | Term Test#2 | Term Test#3 | Concept Quizzes |
|---|---|---|---|---|---|
| Sunita | 80 | 80 | 80 | 82 | 83 |
| Sanjay | 48 | 80 | 80 | 98 | 99 |
It can be very easily verified that, for both sets of data, the mean = 405/5 = 81, the median (the number in the middle) = 80, and the mode (it occurs most often) = 80. However, we also see that Sunita is very consistent, and Sanjay has more variation in his grades. In addition to the central location, we need another piece of information to describe the data: how the numbers are spread out.
We will examine several measures of dispersion (or variation) in this section:
- the range
- the standard deviation (for samples and populations
- the variance (for samples and populations)
- the coefficient of variation
Read on to find out more!
