This tutorial is going to very briefly introduce you, a rule of thumb for the standard deviation, and that has to do with the range. So imagine that you have the heights of the players on the Chicago Bulls basketball team. The range is clearly 13 inches because this person is 84 inches, and he's the tallest. This person, the shortest, is 71 inches tall. So the range is 13 inches.
When we calculate the standard deviation, we end up with 3.83 inches. Now, is there a relationship between those two? Sort of. There's an approximation value. There's a rule of thumb for how the range and standard deviation relate. 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.
And 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. And so it's safer and more predictable to use this rule of thumb without outliers or strong skewness.
So approximate the standard deviation for the heights of the tenors in the New York Choral Society. Scribble this off to the side and pause the video. What you should have come up with first, was that the range was going to be 12. And so, the standard deviation is going to be about 3 inches. And if you put these into a list and actually found the standard deviation, you would find that the standard deviation was about three.
And so to recap, 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.
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.