Measures of Variance
The Range
Learning Objectives
Calculate the range by first calculating the maximum and minimum value in a data set.
The Range, by definition, is the difference between the greatest and smallest values within a data set.
- It is easy to find and easy to understand,
- but only takes into account two of the numbers, the smallest and the largest
- and ignores all the rest.
Let’s look at these 3 sets of numbers:
| Data Set | Value 1 | Value 2 | Value 3 | Value 4 | Value 5 | Value 6 | Value 7 |
|---|---|---|---|---|---|---|---|
| #1 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| #2 | 20 | 21 | 22 | 23 | 24 | 25 | 50 |
| #3 | 20 | 45 | 46 | 47 | 48 | 49 | 50 |
Let’s examine their ranges:
| Data Set | Max Value | Min Value | Range |
|---|---|---|---|
| #1 | 50 | 20 | 50−20 = 30 |
| #2 | 50 | 20 | 50−20 = 30 |
| #3 | 50 | 40 | 50−20 = 30 |
For these 3 sets of numbers, they have the same range of 30, but they are spread out differently.
- In the first set, the numbers are equally spaced.
- In the second set, all the numbers except one are located at the lower end.
- In the third set, all the numbers except one are concentrated at the upper end.
- All the numbers in the middle, between 20 and 50, are ignored.
- For this reason, the range is NOT a very good measure of dispersion, or how the numbers are spread apart.
Let us try this example in Excel:
using the =max() and =min() formulas gives us the ranges shown below:
Key Takeaways: The Range
- It is easy to find and easy to understand
- It only takes into account two of the numbers, the smallest and the largest
- It is simple but not often the best measure of average dispersion/spread of the data
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