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# What are the Range and Standard Deviation?

Learn what the range and standard deviation are, how to calculate them, and why their values are important for interpreting averages.

By
Jason Marshall, PhD
Episode #26

## How to (Really) Calculate Standard Deviation

We’ve now talked about three methods for calculating average values: the mean, median, and mode (affectionately known as the three Ms). So, are we done? Is that everything we could ever want to know about interpreting average values? No, there’s a bit more to it. Today, we’re going to talk about two values that complement averages and help us interpret what they mean: range and standard deviation.

## Do Average Values Tell Us Everything We Need to Know?

Why don’t average values alone tell us everything we need to know about a set of data? Let me answer this question with an example. Imagine you’ve been given the job of comparing the performances of students in high school math classes at two competing schools. Much to the disappointment of the administration at both schools (they’re always looking for good news to boast about), you find that the average math scores are identical for both schools.

Naïvely, it’s tempting to conclude from this that the students at the two schools are performing similarly. But you, being a clever and mathematically informed individual, decide to look a little further into the scores of the individual students. You find that the five math students at the first school (yes, it’s a very small school) received scores of 40, 55, 70, 85, and 100; while the five math students at the second school received scores of 68, 69, 70, 71, and 72. Both of these schools, therefore, have mean and median math scores of 70 (see the articles on how to calculate mean values and how to calculate median values for more information on these two averages), but the individual scores are very different. It’s clear that any fair and complete comparison of the students at these two schools will require more than a simple calculation of average values.