Statistically speaking, standard deviation is just a measure of dispersion or spread in a distribution. For example, the mean score in your class’s chemistry final might be an 85 with a range of say 30 to 95. The range is a measure of dispersion.
Standard deviation is just another way to measure spread.
Standard deviation is useful because we can map it to a bell curve and standardize any specific result. Z-scores normalize how far in units of standard deviation a result is from the mean. This tells us how likely it is to occur or how unusual it is if the data conforms to a Gaussian distribution.
The key point is that in the process of finding the standard deviation, we squared the differences. This will give outliers a higher weight in the computation of variance.
<aside> <img src="/icons/question-mark_blue.svg" alt="/icons/question-mark_blue.svg" width="40px" /> Let’s consider an example
If 49 students score an 85 on a test and 1 scores a zero we see:
mean = 83.3
standard deviation = 11.9
<aside> <img src="/icons/calculator_blue.svg" alt="/icons/calculator_blue.svg" width="40px" /> Computations
</aside>
You’re jumping up and down — “These scores are not distributed like a bell curve!”
There’s a single outlier and everyone else scored the same.
The standard deviation doesn’t feel like a number that represents a typical result. It feels off here.