What is the arithmetic mean of a group of values?
The arithmetic mean distributes the total of all entered values evenly across their count. It describes a centre of balance, but can be pulled strongly by unusually large or small observations.
Balancing a total across its observations
Enter five values. Their sum is divided by five to calculate the arithmetic mean.
The calculator also sorts the values to identify median, highest and lowest values. Range is the highest minus the lowest, showing the full spread but not how values are distributed within it.
When equal weighting is appropriate
Every value contributes equally to the arithmetic mean. If observations represent different quantities or durations, a weighted average may be more appropriate.
Sum divided by count
Sum = Value 1 + Value 2 + Value 3 + Value 4 + Value 5Mean = Sum ÷ 5Checking the mean from total and sample size
The default list is summed and divided by the number of values. Supporting results make the total and count visible so the mean can be checked.
Why averages of averages can be wrong
Do not average averages unless the underlying groups have equal counts. Otherwise each group must be weighted by its number of observations.
- Every entered value has equal weight.
- The list contains comparable quantities in the same unit.
- Blank or invalid entries are handled according to the calculator input rules.
Calculations related to average
The following tools examine neighbouring parts of the same calculation without changing the inputs or assumptions used above.
Quick answers
Frequently asked questions
What is the difference between mean and median?
Mean is the sum divided by five, while median is the middle value after the five entries are sorted.
How is the range calculated?
The lowest entered value is subtracted from the highest.
Can repeated or negative values be used?
Yes. They are included normally in the sum, sort order, median and range.
Educational content only. This guide is not financial advice.