Calculating Standard Deviation

Algebra 2 · Axiom Academy

EXAMPLE Calculating Standard Deviation Work through the five steps — mean, deviations, squaring, variance, and square root — that turn a data set into its standard deviation. Find the standard deviation of the data set 2, 4, 6, 8, 10 , treating these five values as the entire population — so we will divide by N , not N-1 . Excellent work! You've calculated a standard deviation from scratch and seen why each step matters. Standard deviation measures spread: it tells us how far data values typically sit from the mean. We must square the deviations: without squaring, the positive and negative deviations cancel to zero. Variance vs. standard deviation: the variance is in squared units; taking the square root returns us to the original units. The formula: — each part has a purpose. Interpretation: a standard deviation of means data values typically sit about 2.83 units from the mean ( ). Standard deviation is one of the most important measures in statistics — you'll use it to compare data sets, describe distributions, and make predictions.

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