To find the average of three or more numbers, add every value in the list and divide the sum by the total number of values. For example, 12, 18, and 30 have a sum of 60. Dividing 60 by three gives an average of 20.
Enter a list of numbers to calculate the mean, sum, count, median, mode, range, minimum, and maximum.
Include every number in the sum and every observation in the count before completing the division.
The Formula for Three or More Numbers
The arithmetic-mean formula does not change when the list contains three, ten, or one hundred values.
Add the complete list and divide the sum by the number of observations.
The Average Calculator can process values separated by commas, spaces, or new lines.
Worked Example with Three Numbers
Consider the values 12, 18, and 30.
Their sum is 60, and the set contains three observations.
Dividing 60 by three gives an average of 20.
Worked Example with Five Numbers
Suppose the values are 5, 10, 15, 20, and 25.
Adding them gives 75. The count is five.
The average is 75 divided by five, which equals 15.
Why Every Value Must Be Included
The arithmetic mean uses the entire set. Omitting one value changes both the sum and the count.
A repeated value should be included every time it appears because each occurrence is a separate observation.
For 4, 4, 8, and 12, the two occurrences of four must both be counted.
Does the Order of the Values Matter?
The order of the values does not change their arithmetic mean.
The lists 2, 5, 8 and 8, 2, 5 have the same sum and count.
Sorting is useful for finding the median, but it is not required for finding the mean.
Average with Repeated Values
Repeated observations are treated like any other values.
For 3, 3, 3, and 9, the sum is 18 and the count is four.
The average is 4.5, while the mode is three.
Average with Decimal Values
Decimals use the same procedure as whole numbers.
For 1.2, 2.4, and 5.4, the sum is nine.
Dividing nine by three gives an average of three.
Average with Positive and Negative Values
Positive and negative numbers can partially or completely cancel each other.
For minus six, minus three, three, and six, the sum is zero.
Dividing zero by four gives an average of zero.
How More Values Affect the Average
Adding a new value changes both the total and the count.
When the new value equals the current average, the average remains unchanged.
A new value above the current average raises it, while a value below the current average lowers it.
Average vs Average of Two Numbers
For two values, the average is their exact midpoint.
With three or more values, the average remains an equal-share value but is not necessarily the middle observation.
Read How to Find the Average of Two Numbers for the midpoint method.
Common Errors
Do not divide by the wrong count. Count values rather than commas, gaps, or unique numbers.
Do not round individual values too early, because repeated rounding can alter the final result.
When values have unequal importance, use a weighted average rather than a simple arithmetic mean.
Conclusion
To average three or more numbers, add the entire set and divide by the number of observations.
Repeated, negative, and decimal values are included using the same formula.
Use the Average Calculator to calculate the result and related statistics.
FAQs
How do I average three numbers?
Add the three values and divide their sum by three.
How do I average more than three numbers?
Add every value and divide by the total number of values.
Do repeated numbers count separately?
Yes. Every occurrence is included in both the sum and the count.
Does sorting change the average?
No. Rearranging the same values does not change their sum or count.
Can the average be a number not in the list?
Yes. The arithmetic mean does not need to match an original observation.