2.3 Standard Deviation

Notes

The standard deviation $s$ measures the typical distance of values from the mean. Larger $s$ means more spread.

• $\displaystyle s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}}$
• Steps: find $\bar{x}$, find each deviation $x - \bar{x}$, square them, add, divide by $n - 1$, take the square root.
• Example: 5, 9, 13 has $\bar{x} = 9$. Squared deviations: 16, 0, 16, total 32. $\displaystyle \frac{32}{2} = 16$, so $s = 4$.
• Adding a constant to every value changes the mean but not $s$. Multiplying every value by $k$ multiplies both the mean and $s$ by $|k|$.