Average (arithmetic mean)
A = S / n, where S is the sum of all of the terms in the set, n is the number of terms in the set, and A is the average.
Arithmetic Mean
See average (above).
Weighted average
In a weighted average, some data points contribute more than others to the overall average. This is in contrast to a regular average, in which each data point contributes equally to the overall average. A weighted average can be expressed with the formula A = [(D1)(W1) + (D2)(W2) + … + (Dn)(Wn)] / sum of weights, where each D represents a distinct data point, each W represents the weighting assigned to that data point, and A is the weighted average.
Median
Literally, the “middle” value in a set of numbers written in increasing (or decreasing) order. In a set with an odd number of terms, the median is the middle number. In the set 1, 3, 4, 6, 9, the median is 4. In a set with an even number of terms, the median is the average of the two middle numbers. In the set, 1, 3, 4, 6, the median is (3+4)/2 = 3.5.
Standard Deviation (SD)
A measurement used to describe the how far apart numbers in a set are. This is also called the “spread” or the “variation” of the set. Technically, SD is a measure of how far from that set’s average the data points typically fall. SD can be either positive or zero.
- A small SD indicates that the terms of the set are clustered closely around the average value of that set.
- A large SD indicates that the terms of the set are widely spread, with some terms very far from the average value of that set.
- An SD of zero indicates that all of the terms of that set are exactly equal to that set’s average.
