*47*

TheÂ **range rule of thumbÂ **offers a quick and easy way to estimate the standard deviation of a dataset by using the following formula:

**Standard deviation = range / 4**

This rule of thumb is sometimes used because it allows you to estimate the standard deviation of a dataset by simply using two values (the minimum value and maximum value) instead of every value.

**Example: Range Rule of Thumb**

Suppose we have the following dataset of 20 values:

**4, 5, 5, 8, 13, 14, 16, 18, 22, 24, 26, 28, 30, 31, 31, 34, 36, 38, 39, 39**

The actual standard deviation of these values isÂ **11.681**.

Using the range rule of thumb, we would estimate that the standard deviation is (39-4) / 4 =Â **8.75**. This value is somewhat close to the actual standard deviation.

**Cautions on Using the Range Rule of Thumb**

The obvious advantage of the range rule of thumb is that itâ€™s incredibly simple and quick to calculate. All we need to know is the minimum value and the maximum value of the dataset.

The drawback of the range rule of thumb is that tends to only work well when the data comes from a normal distribution and the sample size is around 30. When these conditions donâ€™t hold, the range rule of thumb doesnâ€™t perform well.

**Alternative to the Range Rule of Thumb**

In a 2012 article from the *Rose-Hulman Undergraduate Mathematics Journal*, Ramirez and Cox suggested using the following formula as an improvement over the range rule of thumb:

**Standard deviation = range / (3âˆš(ln (n))-1.5)**

whereÂ *nÂ *is the sample size.

Consider the same dataset we used before:

**4, 5, 5, 8, 13, 14, 16, 18, 22, 24, 26, 28, 30, 31, 31, 34, 36, 38, 39, 39**

Using this formula, we would calculate the standard deviation as ** 35/ (3âˆš(ln(20))-1.5)Â **= **9.479**. This value is closer to the actual standard deviation ofÂ **11.681** compared to the range rule of thumb estimate ofÂ **8.75**.

This formula is a bit more complicated to calculate than the range rule of thumb, but it does tend to provide a more accurate estimate of the standard deviation when the data does not come from a normal distribution or when the sample size is not close to 30.

**Additional Resources**

Range Rule of Thumb Calculator

Measures of Dispersion: Definition & Examples