What is the Range Rule of Thumb?
The range rule of thumb allows you to estimate the standard deviation of a dataset quickly. This process is not as accurate as the actual calculation for the standard deviation, but it’s so simple you can do it in your head.
Use this method when you need a rough estimate quickly or have a dataset summary that doesn’t provide enough information to calculate the actual standard deviation.
The range of a dataset is simply the maximum value minus the minimum value. So, you can estimate the StDev knowing only those two values.
The range and standard deviation are both measures of variability, but there is no precise mathematical relationship between the two. However, you can use the range to estimate the standard deviation.
Range Rule of Thumb Formula
The range rule of thumb formula is the following:
Subtract the smallest value in a dataset from the largest and divide the result by four to estimate the standard deviation.
In other words, the StDev is roughly ¼ the range of the data.
Let’s apply the range rule of thumb formula to actual data. From a research study I helped run, I have a dataset containing 88 heights. Download the Excel data file: RangeRuleofThumb.
Excel’s descriptive statistics say the height data have the following properties:
- Mean: 1.51m
- Standard Deviation: 0.07m
- Maximum: 1.66m
- Minimum: 1.33m
Now suppose you’re reading a summary of the height dataset. While the summary includes the maximum and minimum value, pretend it doesn’t list the StDev. Let’s try it out!
Voila, you have estimated the StDev using two numbers from the dataset!
The range rule of thumb’s estimate (0.08) is close to the correct standard deviation of 0.07.
How Does the Range Rule of Thumb Work?
It might seem odd that you can just divide the range by four to estimate the standard deviation. However, the range rule of thumb uses the properties of the normal distribution and the empirical rule.
When data follow the normal distribution, the empirical rule states that 95% of the values fall between the mean ± 2 StDevs.
Given these properties, virtually all values in a sample fall within a four standard deviation spread that centers on the mean.
Therefore, the range of a dataset approximates the four StDev spread. Hence, dividing the range by four approximates one StDev.
By understanding how it works, you can work out its limitations. The range rule of thumb:
- Works best with data that at least roughly follow a normal distribution.
- Is sensitive to outliers. One unusually high or low value can affect the estimate.
- Depends on the sample size. Very small samples tend to underestimate, while very large samples overestimate.
- Does not produce more precise estimates with larger sample sizes, unlike most estimates.