4: How do we measure variation? If you said standard deviation…

You’re on the right track!

Do you remember how to calculate a standard deviation (SD)? If not, there’s a quick review below.

Of course, the easy way to do this is to use your calculator or a spreadsheet, assuming that’s ok with your instructor. However, it is important to understand what the standard deviation is doing. Basically, it accounts for how far each data point is from the group average. For example, the smallest fish in the Fish-2-Whale group gained 212g, or 55 grams less than the average while the largest fish gained 324g, or 57 grams more than the average. These are the “deviations” from average.

examples of deviation

It would be convenient if we could just average the deviations, but unfortunately it’s not quite that simple.  Instead, we square each deviation (partly to get rid of the plus or minus signs), average the squares (except that we divide by n-1 rather than n), and then take the square root of that number. (So, in short form: square, average, square-root).  The result of that is the standard deviation.  The formula for the sample standard deviation looks scary, but it’s really just the above steps: Ttest_eqn_Page_1

What is the stardard deviation for the Fish-2-Whale gains?


212 221 240 241 283 297 318 324


First click: suggested course of action.
Second click: details of that step.

Step Details

If you repeat the calculation for the control group, that is the group that were not given the Fish-2-whale food, you will get a standard deviation of 28 g.