How to calculate the average
The average most people mean is the arithmetic mean: add all the numbers together and divide by how many numbers there are.
Example: test scores 72, 85, 90, 66 and 85.
- Sum: 72 + 85 + 90 + 66 + 85 = 398
- Count: 5
- Mean: 398 ÷ 5 = 79.6
Mean vs. median vs. mode
| Measure | How to find it | Best used when |
|---|---|---|
| Mean | Sum ÷ count | Data is fairly symmetrical with no extreme outliers (test scores, temperatures) |
| Median | Middle value after sorting (average of the two middle values if the count is even) | Data is skewed or has outliers (home prices, incomes) |
| Mode | Most frequent value | Categories or repeated values (shoe sizes, most common rating) |
Example of why it matters: five salaries of $40k, $45k, $50k, $55k and $400k have a mean of $118k but a median of $50k. The median describes the typical person far better.
Finding the median: sort 72, 85, 90, 66, 85 → 66, 72, 85, 85, 90. With five values the median is the 3rd one: 85. For six values, average the 3rd and 4th.
How to calculate a weighted average
In a weighted average some values count more than others. Multiply each value by its weight, add the results, and divide by the total of the weights.
Example — course grade: homework 92 (worth 20%), midterm 78 (30%), final 85 (50%).
- (92 × 20) + (78 × 30) + (85 × 50) = 1,840 + 2,340 + 4,250 = 8,430
- Total weight: 20 + 30 + 50 = 100
- Weighted average: 8,430 ÷ 100 = 84.3
A simple average of 92, 78 and 85 would be 85 — the heavier weight on the lower midterm pulls the real grade down.
How to calculate averages in Excel and Google Sheets
| What you want | Formula |
|---|---|
| Average (mean) | =AVERAGE(A2:A20) |
| Median | =MEDIAN(A2:A20) |
| Mode | =MODE.SNGL(A2:A20) (or =MODE.MULT for several modes) |
| Weighted average | =SUMPRODUCT(A2:A20, B2:B20) / SUM(B2:B20) |
| Average ignoring zeros | =AVERAGEIF(A2:A20, "<>0") |
| Average matching a condition | =AVERAGEIF(B2:B20, "East", C2:C20) |
| Standard deviation (sample) | =STDEV.S(A2:A20) |
A common mistake is averaging averages. If one class of 10 students averaged 80 and another class of 30 averaged 70, the overall average is not 75 — it's (10 × 80 + 30 × 70) ÷ 40 = 72.5. Use a weighted average with class size as the weight.
Other statistics shown
- Range: largest value minus smallest value — a quick measure of spread.
- Standard deviation: how far values typically sit from the mean. Use the sample version when your numbers are a sample of a bigger group, and the population version when you have every value.
- Geometric mean: the nth root of the product of n values — the right average for growth rates and investment returns (all values must be positive).
Frequently asked questions
How do you find the average of a set of numbers?
Add all the numbers and divide by how many there are. The average of 4, 8 and 12 is (4 + 8 + 12) ÷ 3 = 8.
What is the difference between average and median?
The average (mean) is the sum divided by the count; the median is the middle value when sorted. Outliers pull the mean but barely move the median.
What if there is no number that repeats?
Then the set has no mode. If two or more values tie for most frequent, the set is bimodal or multimodal and all of them are modes.
How do I calculate an average percentage?
If each percentage is based on the same total, average them normally. If the totals differ, add up the underlying numbers first — for example (45 + 18) ÷ (50 + 30) = 78.75% — rather than averaging 90% and 60%.
How do I calculate a weighted average in Excel?
Put values in column A and weights in column B, then use =SUMPRODUCT(A2:A10,B2:B10)/SUM(B2:B10).