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Range Rule of Thumb

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This tutorial will introduce a rule of thumb for the standard deviation that has to do with the range. You will learn about:

- The range rule of thumb

Imagine that you have the heights of the players on the Chicago Bulls basketball team.

The range is clearly 13 inches because the tallest player is 84 inches and the shortest is 71 inches tall. So the range is 13 inches: the smallest value subtracted from the highest.

When you calculate the standard deviation, you end up with 3.83 inches. Is there a relationship between those two measurements? There's an approximation value. There's a **“rule of thumb” **for how the range and standard deviation relate.

**Range "Rule of Thumb"**- In a set of data, the standard deviation is approximately one-fourth the difference between the largest and smallest number in the data set. This rule of thumb is more accurate for larger samples with distributions that are approximately symmetric.

Standard deviation is approximately one fourth the size of the range. Conversely, if you wanted to switch it around, the range is going to be about four standard deviations wide.

- Range "Rule of Thumb"

This rule of thumb works best for data sets that have no outliers and are roughly symmetric. Skewness and outliers can both greatly affect both the range and the standard deviation. It's safer and more predictable to use this rule of thumb without outliers or strong skewness.

Approximate the standard deviation for the heights of the tenors in the New York Choral Society. Here is a list of those heights:

69, 72, 71, 66, 76, 74, 71, 66, 68, 67, 70, 65, 72, 70, 68, 73, 66, 68, 67, 64

- First, what did you calculate as the range? You likely noticed that the range is 12.
- Using that measurement and the “rule of thumb,” what is the standard deviation? About 3 inches.

If you put those heights into a list and calculated the standard deviation, you would find that the standard deviation was about three, so the rule of thumb works here.

The **range rule of thumb** for standard deviations is that the standard deviation is approximately one fourth the range. Equivalently, the range is four times the standard deviation, approximately. The rule of thumb is best applied for fairly small distributions, roughly symmetric, free of outliers.

Good luck, and we'll see you next time.

Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS