Sample standard deviation (s)

How to read it

OpenStax’s Introductory Statistics puts the pair in one sentence: “The lower case letter s represents the sample standard deviation and the Greek letter σ (sigma, lower case) represents the population standard deviation.” If the sample has the same characteristics as the population, OpenStax adds, s should be a good estimate of σ. s is the square root of the sample variance s². NIST’s Engineering Statistics Handbook defines it the same way, as the square root of the squared distances from the mean added up and divided by one less than the number of values, and notes that taking the root restores the units of the original data.

Also searched as: s, sample standard deviation symbol, s in statistics, standard deviation symbol.

Sx and σx on a calculator

Calculators and statistics software often show both. On the TI calculator screen reproduced in OpenStax’s textbook, one-variable statistics for the same 26 values give Sx = 3.500549407 and, below it, lower-case sigma x = 3.432571103. Sx is the sample standard deviation, OpenStax’s s. The σx line treats the data as the whole population, which OpenStax’s method divides by N rather than n − 1, so it comes out a little smaller.

Look-alikes

The small Greek σ is the population standard deviation, and its square, σ², the population Variance (s² σ²).