Definitions:

From Wolfram MathWorld:

Mean, median, and mode are kinds of "averages".

Average – The numerical result of dividing the sum of two or more quantities by the number of quantities.

Mean - The average of a number of items in a group.

Median - The middle item in an ordered group. If the group has an even number of items, the median is the average of the two middle terms.

Mode -The value that occurs most often. If no number is repeated, then there is no mode for the list.

Arithmetic Mean -- from Wolfram MathWorld

A general example to help you recognize patterns and spot the information you're looking for

If there is a set A such that $$A={ 13, 18, 11, 14, 15, 21, 13}$$ The mean is the usual average: $${13 + 18 + 11 + 15 + 14 + 21 + 13 \over 7 }= 15$$ The median is the middle value: $${11, 13, 13, 14, 15, 18, 21}= 14$$ The mode is the number that is repeated more often than any other, so the mode $$=13$$

We use them when we want to find the trend. Data is collected historically and inferences are made. These all are measures of central tendency - a single value that attempts to quantify the "average" value around which the values in a data set tend to cluster.

Averages

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Mean, Median and Mode

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