In standard deviation calculation, what do you do with the differences from the mean?

In the calculation of standard deviation, the differences from the mean, which are also known as deviations, are squared. This step is crucial because squaring the differences ensures that all values are non-negative. If you simply summed the differences without squaring them, you would end up with a value that could be misleading, as the positive and negative differences might cancel each other out, yielding zero or a very small number that does not accurately represent the variability in the data set.

By squaring each deviation, the impact of larger deviations is amplified, making them more significant in the overall calculation. This approach allows the standard deviation to provide a true representation of how spread out the values are around the mean. Once all the squared differences are obtained, they are then averaged and the square root of that average is taken to calculate the standard deviation, which ultimately gives us a measure of data dispersion.