How to Find an Average

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How to Find an Average
Teachers, business owners, and scientists all have to deal with large groups of numbers.  Grades, money values, and numerical arrays often need to be combined to find a common value that they all share.  To make computations and calculations easy, many people rely on averages.

What is an Average?
The average is a mathematical value that determines the common value of a set of numbers.  Averages are also called measures of central tendency. Many mathematical and statistical operations use the average as a starting point for many other calculations, including deviations and variations.  Average values can also be used to give a person an overview of the values that can be derived from the array.

Types of Averages
There are three measures of central tendency that you should know:

The arithmetic mean is a measure of central tendency where the sum of all the values in a given set of numbers is determined by the number of elements in that set.
The mode is a measure of central tendency that is determined by the value most often repeated in a given set of numbers.
The median is the middle value of a finite group of numbers ranked in ascending or descending order.
Computing for Averages
Most people understand the average in terms of the arithmetic mean.  The arithmetic mean is particularly useful if you want to have a birds-eye view of a given set of numbers.  Here’s how you can compute the arithmetic mean:

Start by gathering all the scores you need to find the average for.  You do not have to rank the values in order.  Make sure not to eliminate duplicate scores.
Compute for the sum of all the scores.  Take note of the sum, and mark this value with a notation for a variable (usually “x”).
Count how many elements are there in the array.  Take note of the number of elements, and mark this value with a unique notation for a variable (usually “n”).
The value of the arithmetic mean is derived by dividing x over n. After you have carefully added the elements to form x and counted the elements to form n, divide x by n and you’ll have the arithmetic mean.
The average is one of the most useful mathematical concepts that can give you many useful values to work with.  With the average, you can have a good idea of what you can do with a seemingly meaningless and confusing set of scores and numbers.

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