Standard Deviation

What does standard deviation measure?

How spread out the values in a data set are from the mean — a low standard deviation means values are close to the mean, a high one means they're spread out

What is variance, in relation to standard deviation?

The average of the squared deviations from the mean — standard deviation is the square root of the variance

If a data set has a standard deviation of 0, what does that tell you?

All the values in the data set are identical (equal to the mean)

What are the steps to calculate standard deviation?

Find the mean, find each value's deviation from the mean, square each deviation, average the squared deviations (variance), then take the square root

Why do we square the deviations when calculating standard deviation, instead of just averaging them directly?

Because deviations above and below the mean would cancel each other out to zero if not squared — squaring makes them all positive before averaging