The range of a single number is 0.
Understanding Range
In mathematics and statistics, the range is a simple measure of spread or variability within a dataset. According to standard definitions, including insights from resources on the topic, the range is found by subtracting the lowest value from the highest value in a set of numbers.
- Highest Value: Also known as the largest value, largest number, or maximum value.
- Lowest Value: Also known as the smallest value, smallest number, or minimum value.
Formula:
Range = Highest Value - Lowest Value
Calculating Range for One Number
When your dataset consists of only a single number, that number is simultaneously the highest value and the lowest value in the set.
Let's consider a dataset containing just one number, for instance, the number 7.
- The dataset is {7}.
- The highest value in this dataset is 7.
- The lowest value in this dataset is 7.
Applying the formula for range:
Range = Highest Value - Lowest Value
Range = 7 - 7
Range = 0
This holds true for any single number. The difference between a number and itself is always zero.
Example Calculation
Here's how the range is calculated for a single number:
| Dataset | Highest Value | Lowest Value | Calculation | Range |
|---|---|---|---|---|
| {15} | 15 | 15 | 15 - 15 | 0 |
| {-4} | -4 | -4 | -4 - (-4) | 0 |
| {0.5} | 0.5 | 0.5 | 0.5 - 0.5 | 0 |
Why the Range is Zero
The range is a measure of the distance between the extreme points in a dataset. When there's only one point (a single number), there is no distance or spread between values, as there's only one value present. Therefore, the range, which quantifies this spread, is zero. It indicates no variability within a dataset of one element.
