How the range rule of thumb works
The range rule of thumb gives a quick estimate of the standard deviation as (maximum − minimum) ÷ 4. It rests on the fact that for many data sets nearly all values lie within about four standard deviations. For a maximum of 100 and a minimum of 20, the range is 80, so the estimated standard deviation is 80 ÷ 4 = 20. It is an estimate, so treat it as a sanity check on the exact figure from the standard deviation calculator.
How to use this calculator
Enter the maximum and minimum values of your data. The result shows the estimated standard deviation and the range it came from. For an exact standard deviation from the full data set, you would compute it from every value rather than just the extremes.
When the estimate is useful
The rule is handy for a fast sanity check or when you only know the range, not every value. It is most accurate for roughly bell-shaped data and moderate sample sizes; it can be off for very small or very large samples or skewed data. To quantify skew, see the skewness calculator, and pair the estimate with the mean, median, mode calculator for the centre.
Frequently asked questions
- How do I use the range rule of thumb?
- Subtract the minimum from the maximum and divide by 4. For max 100 and min 20, that is 80 ÷ 4 = 20.
- Why divide by 4?
- Because for many bell-shaped data sets almost all values fall within about four standard deviations of the mean.
- How accurate is the range rule of thumb?
- It is a rough estimate. It works best for roughly normal data and moderate sample sizes and can be inaccurate for very small, large or skewed samples.
- Does it replace the exact standard deviation?
- No. It is a quick approximation. For precision, compute the standard deviation from every value in the data set.
- Can I run it backwards to estimate the range?
- Yes — multiplying a known standard deviation by 4 gives a rough expected spread between the smallest and largest values. It is often used the other way round as a check: if the actual range is far more than four standard deviations, suspect an outlier.