Math Concepts

An average is a statistic that is used to summarize data. The most common type of average is the arithmetic mean. The average (arithmetic mean) of a list of n numbers is equal to the sum of the numbers divided by n.

For example, the mean of 2, 3, 5, 7, and 13 is equal to            

                        .

When the average of a list of n numbers is given, the sum of the numbers can be found. For example, if the average of six numbers is 12, the sum of these six numbers is 12 x 6, or 72.

The median of a list of numbers is the number in the middle when the numbers are ordered from greatest to least or from least to greatest. For example, the median of 3, 8, 2, 6, and 9 is 6 because when the numbers are ordered, 2, 3, 6, 8, 9, the number in the middle is 6. When there is an even number of values, the median is the same as the mean of the two middle numbers. For example, the median of 6, 8, 9, 13, 14, and 16 is the mean of 9 and 13, which is 11.

The mode of a list of numbers is the number that occurs most often in the list. For example, 7 is the mode of 2, 7, 5, 8, 7, and 12. The list 2, 4, 2, 8, 2, 4, 7, 4, 9, and 11 has two modes, 2 and 4.

Note: On the SAT, the use of the word average refers to the arithmetic mean and is indicated by "average (arithmetic mean)." The exception is when a question involves average speed (as in this problem from the Number and Operations review). Questions involving median and mode will have those terms stated as part of the question's text.

Probability refers to the chance that a specific outcome can occur. When outcomes are equally likely, probability can be found by using the following definition:

For example, if a jar contains 13 red marbles and 7 green marbles, the probability that a marble selected from the jar at random will be green is

If a particular outcome can never occur, its probability is 0. If an outcome is certain to occur, its probability is 1. In general, if p is the probability that a specific outcome will occur, values of p fall in the range 0 $\le$ p $\le$ 1. Probability may be expressed as either a decimal, a fraction, or a ratio.