Standard Deviation

The mean The mean of a sample, is denoted: (“x-bar”) If a mean is taken for an entire population it is denoted: (“mu”)

The n deviations from the sample mean are the differences: The sum of all of the deviations from the sample mean will be equal to 0 (zero), except possibly for the effects of rounding the numbers. This means the average deviation will not be of use as a measure of variability.

Variance We can “trick” the numbers into being of use by squaring each deviation, or: The sample variance, denoted s 2, is the sum of the squared deviations from the mean, divided by (n-1).

Standard Deviation The variance can be used as a measure of variability, but because the units are squared it is not in the same scale as the original observations. Take the square root of the variance to return to the original scale, and you have the sample Standard Deviation, s.

For a population, the standard deviation is denoted by σ (sigma), and the population variance is denoted σ 2 SamplePopulation s and s 2 σ and σ 2

Example: Swing for the Fences…. Below are the number of home runs this season hit by the Padres starting lineup 8/24/1. Find the mean, variance, and standard deviation. NameHR Everth Cabrera2 Will Venable8 Chase Headley22 Carlos Quentin14 Yonder Alonso7 Logan Forsythe3 Cameron Maybin6 John Baker0 Andrew Werner0