③ Why it works

Standard deviation is the “typical distance” of a value from the mean. We square each deviation so negatives don’t cancel positives, average those squares (that’s the variance), then take the square root to get back to the original units. Use population SD (÷ N) when your data is everyone you care about; use sample SD (÷ N−1) when your data is a sample estimating a larger group — dividing by N−1 corrects the slight underestimation that sampling causes.