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The Range Rule of Thumb is a method used by investors to measure the volatility of a security. It looks at the highest and lowest prices of a security over a given period of time, and then divides the difference between the two by the average price in order to calculate the range of the security. This can be used to help investors gauge the volatility of a security and make informed decisions about their investments.
The range rule of thumb 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 is 11.681.
Using the range rule of thumb, we would estimate that the standard deviation is (39-4) / 4 = 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 it’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 don’t hold, the range rule of thumb doesn’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 / (3√(ln(n))-1.5)
where n 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
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.
Range Rule of Thumb Calculator
Measures of Dispersion: Definition & Examples