# Video: Finding the Standard Deviation of a List of Data Values

Learn through examples that standard deviation is a very useful measure of the variability within a set of data. Also, learn how to use the formula in two different formats to calculate the standard deviation of a list of data values.

11:32

### Video Transcript

In this video, we talk briefly about what standard deviation is, a measure of the variability of a set of data. And then we move on to see how to calculate the standard deviation from a list of data values. Here, we’ve got three sets of test results, scores out of ten for three different groups of nine students. How can we describe the differences in the results between the groups? Which group did best? Which did worst? What are the differences? Well first, we could work out the mean score for each group; add up the scores and divide by how many there are. Well, if we say 𝑥 is the value of a score of an individual, this Σ, this funny sign here in front of the 𝑥, means add up all the 𝑥-values: add up all the scores for a particular group. And then 𝑛 is simply the number of people in each group, and that’s nine students in each case. Now it turns out with this particular set of data, whether I go for group 𝐴 or 𝐵 or 𝐶, if I add up all their scores, I get the same answer, forty-five. So in all three cases, my mean score is gonna be forty-five divided by nine, which is five. So my mean score in all three groups is five. So on average, they all did the same.

Okay, let’s work out the median score for each group. And to do that, we need to organize them in order from smallest to largest in each group and look at the middle score. The middle person in each case has got four students to the left and four students to the right. And again in all three cases the median score here is five. So again we’re saying, on average, all three groups did the same. Right, well now we can start to look at the variability of the data. Well in group 𝐵, everybody scored exactly five. That’s a very consistent performance across the group. There was zero variability in their scores. But in groups 𝐴 and 𝐶, there was some variation between individuals.