Most often, when someone wants to find the average of a set of numbers, he will find the mean. To do so, he will add all the numbers in the set together, and then divide by the number of data in the set. The result is the mean.
For example, to find the mean of 14, 17, 21 and 25, first add them all together. This equals 77. Next, divide 77 by four, the number of numbers you just added. The result is 19.25, and that is the mean of the number set.
A set of numbers can only have one mean, which makes it useful for comparing multiple sets of data; however, a single number can have a large impact on the mean of the set.
The median of a number set is the number in the middle of the set. To find the median, arrange all the numbers in order from least to greatest, count them and find the number that is exactly halfway through the set. If the set has an even count of numbers in it, find the two that are in the middle and then find the mean of those two numbers. The result is the median.
For example, to find the median of 11, 17, 14, 21 and 19, begin by putting them in order: 11, 14, 17, 19, 21. Then, count them -- there are five numbers in the set. The number in the middle is 17, so that is the median of the set. If the set only has four numbers in it -- 11, 14, 17 and 19, for example -- find the two numbers in the middle (14 and 17), add them together (31), and then divide that number by two. The result, 15.5, is the median of the set.
Medians are also useful for comparing sets of data, and they are less easily affected by one or two numbers.
The number that appears the most times in a set of numbers is the mode. Sets can have one mode, more than one mode or no mode.
In the set 17, 15, 16, 15, 19 and 20, the only number that appears more than once is 15, so 15 is the mode.
In the set 17, 15, 16, 15, 16, 19 and 20, both 15 and 16 appear two times. They are both modes of the set.
In the set 17, 15, 16, 19 and 20, each number appears only once, so the set has no mode.
Because a set can have more than one mode, it is a less definitive answer than the other two and less easily used to compare sets.
The most basic way to find the average of a set of numbers is to find its mean. But sometimes the particular data involved can skew the mean so it isn't really representative of the average. For example, if most of the numbers are very similar, but there is one number that is much bigger or much smaller than the others, that one number will skew the mean away from the useful average. Such a number is called an outlier. In that case, statisticians use the median to find the average of the set.
The mode is most useful when the set isn't actually a set of numbers, but rather of some other form of data. For example, if a researcher takes a survey of people's favorite foods, he cannot find the mean or median of their answers, but he can find the mode to determine the most frequent result.