how to find the mean in math

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In mathematics, the "mean" is a kind of average found by dividing the sum of a set of numbers by the count of numbers in the set.^[1] While it isn't the only kind of average, the mean is the one most people think of when speaking about an average. You can use means for all kinds of useful purposes in your daily life, from calculating the time it takes you to get home from work, to working out how much money you spend in an average week.^[2]

Steps

1
Determine the set of values you want to average. These numbers can be big or small, and there can be as many of them as you want.^[3] Just make sure you are using real numbers and not variables.
- Example: 2, 3, 4, 5, 6.
2
Add your values together to find the sum. You can use a calculator, by hand, or a spreadsheet application to do so.^[4]
- Example: $2+3+4+5+6=20$
3
Count the number of values in your group. Count all of the numbers added up. Identical values should still be counted, meaning if you have values that repeat in your set, each one still counts in determining your total. Do not include the sum (answer) of all the numbers added up when counting the quantity of the values.^[5]
- Example: 2, 3, 4, 5, and 6 make for a total of five values.
4

Divide the sum of the set by the number of values. The result is the mean (a type of average) of your set. This implies that if each number in your set was the mean, they would add up to the same total.^[6]

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Question

What do I do if my mean/average has a remainder?

Convert the remainder to a decimal or fraction. For example: the average of 5, 12, and 17 is 34 ÷ 3, which is 11 with a remainder of 1. Convert the remainder to the fraction 1/3 or the decimal .33. Thus, the average is 11-1/3 or 11.33.
Question

How do I calculate the mode?

It is the number in a set which appears most often. In the set {1 7 9 0 4 5 4}, 4 is the mode.
Question

How do I find the range?

The range of a data set is the difference between the largest number and the smallest number in the set.
Question

What if there's a remainder?

That's fine. A mean does not have to be a whole number.
Question

How do you find the mean with negative numbers?

Add them algebraically, and divide by the number of numbers.
Question

How do I calculate the mean of 45, 12, 15, 92 and 61?

Add them all together and divide the answer by five (since there are five numbers).
Question

How do I find the median?

Add the highest number and the lowest number and divide by two.
Question

How do I calculate survey results?

Assuming the survey responses consist of numbers, add the numbers together, and divide by the number of responses.
Question

Can a mean be a decimal point?

Yes.
Question

Does this work for all numbers?

It works for all rational numbers.

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Other kinds of averages include the median and mode.^[7] The mode is the value repeated most often in any set. The median is the number in a set with an equal quantity of values in the set greater and smaller than it. These averages will often produce different results than the mean from the same set of numbers.^[8]

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To calculate the mean of a set of numbers, start by adding up all of the values together to find the sum. Then, count all of the numbers that you added up. Finally, divide the sum of the set by the number of values to get the mean. If you want to learn what to do if the mean has a remainder, keep reading the article!

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