standard deviation

what is standard deviation

Standard Deviation( $s$ ) – a way of measuring the typical deviation (distance) of each observation from the mean

Mathematically:

s = \sqrt{\frac{1}{n - 1} \sum (x_{i} - \bar{x})^{2}}

Why do we take the square root? Taking the square root ensures that the standard deviation has the same units as the original variable

Why do we use n-1 and not n? It’s complicated. Using n-1 gives us better estimates and predictions

measures spread (variability) from the mean
- values close to the mean = smaller contribution to s
- values far away from the mean = larger contribution to s
Cannot be negative
has the same units as the original variable