Although the 5 number summary is very useful for describing a data set, it is not the most widely used. The most common measures are the mean for the center and the standard deviation to measure spread. Standard deviation measures how far the observations are from their mean.

* The variance of a set of observations is the average of the squares of the deviations of each observation from the mean. * The standard deviation (s) is simply the square root of the variance. Your TI-83 calls this Sx.

* Seven men took part in a study of metabolic rates. Here are the calories burned in 24 hours by the men: * Find s. * s=189.24

* The sum of the deviations from the mean will always be 0. This is why we square and square root when finding s.

* Now the question comes up as to why we divide by n-1 instead of n. Because the sum of the deviations is always 0, the last deviation can be found once we know the first n-1 deviations. Since only n-1 of the squared deviations can vary freely, we average by dividing the total by n-1. The number n-1 is called the degrees of freedom of the variance or standard deviation.

1. s measures spread about the mean - so, use s only when using xbar. 2. s=0 if there is no spread (ie, all observations are the same). Else, s>0. A big s value implies the data are spread out. 3. s is nonresistant.

* The five number summary is usually better than the mean and standard deviation for describing a skewed distribution. * Use x-bar and s for reasonably symmetric distributions. * Remember, always graph the data!