Learn in the textbookDescriptive Statistics (Measures of Central Tendency and Dispersion)
DefinitionThe standard deviation (標準偏差) is the positive square root of the variance, expressing spread in the same unit as the original data.
ExplanationBecause variance squares the deviations, its unit is squared as well (for test scores, "points squared"). Taking the square root brings the standard deviation back to the original unit, so it can be set side by side with differences from the mean.
AnalogyJust as you recover a side length from an area, the standard deviation brings the squared-up variance back to the original ruler.
Memory hookRead it as the "standard" deviation: a rough gauge of how far a typical value sits from the mean.