Friday, April 27, 2007

Mean, Median, Mode, Midrange and Standard Deviation

A definition of terms to help my frail memory when I need it most :)

The arithmetic mean is the sum of the numbers, divided by the quantity of the numbers.

The geometric mean of two numbers is the square root of their product.The geometric mean of three numbers is the cubic root of their product.

The quantity obtained by adding the largest and smallest values and dividing by 2, statisticians call the midrange.

The median is the central point of a data set. To find the median, you would list all data points in ascending order and simply pick the entry in the middle of that list. If there are an even number of observations, the median is not unique, so one often takes the mean of the two middle values.

The standard deviation is the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. If the data points are close to the mean, then the standard deviation is small. Conversely, if many data points are far from the mean, then the standard deviation is large. If all the data values are equal, then the standard deviation is zero.It is defined as the square root of the variance.

For lists, the mode is the most common (frequent) value. A list can have more than one mode. For histograms, a mode is a relative maximum ("bump"). A data set has no mode when all the numbers appear in the data with the same frequency. A data set has multiple modes when two or more values appear with the same frequency.A distribution with two modes is called bimodal. A distribution with three modes is called trimodal.