Average Calculator
Type one number per row. The mean is the sum divided by how many numbers there are; the median is the middle number once they are sorted. The calculator shows both, plus the range from smallest to largest.
Answer
Mean (average)
80
Of 5 values adding up to 400.
- median
- 85
- smallest to largest
- 68 – 90
- range
- 22
Check the work
Every line comes from the same calculation as the answer.
mean = sum ÷ count; median = middle of the sorted list
| sum | 72 + 85 + 90 + 68 + 85 | 400 |
|---|---|---|
| mean | 400 ÷ 5 | 80 |
| median | middle of 68, 72, 85, 85, 90 | 85 |
| range | 90 − 68 | 22 |
How it works
For 72, 85, 90, 68 and 85 the sum is 400, and 400 ÷ 5 = 80, so the mean is 80. Sorted, the list reads 68, 72, 85, 85, 90 and the middle number is 85, so the median is 85.
The two answers differ because the mean uses every value’s size while the median only uses its position. One unusually large or small number moves the mean a long way and the median hardly at all, which is why salaries and house prices are usually reported as medians.
When the mean and median are far apart, the calculator says so. That gap is a quick signal that the list is lopsided and that a single “average” would hide something.
Formula
mean = (x₁ + x₂ + … + xₙ) ÷ n; median = middle of the sorted list
With an odd number of values the median is the single middle one; with an even number it is halfway between the two middle values.
Worked examples
- Try these numbers
Five test scores
- 72 + 85 + 90 + 68 + 85 = 400.
- 400 ÷ 5 = 80.
- Sorted: 68, 72, 85, 85, 90 — the middle value is 85.
Mean 80, median 85, range 22.
- Try these numbers
An even number of values
- 3 + 9 + 4 + 10 = 26, and 26 ÷ 4 = 6.5.
- Sorted: 3, 4, 9, 10 — the middle pair is 4 and 9.
- (4 + 9) ÷ 2 = 6.5.
Mean 6.5 and median 6.5.
- Try these numbers
Five salaries with one outlier
- The five salaries add up to 299,000.
- 299,000 ÷ 5 = 59,800.
- Sorted, the middle salary is 36,000.
Mean 59,800 but median 36,000 — four of the five people earn less than the mean.
Inputs and results
- Values
- The numbers to summarise, one per row, all in the same unit.
- Mean
- The sum divided by the count.
- Median
- The middle value of the sorted list.
- Range
- Largest value minus smallest value.
When to use it
- Averaging test or quiz scores when every one counts the same.
- Comparing a typical monthly bill with an unusually expensive month.
- Summarising measurements such as daily step counts, commute times or sale prices.
Common mistakes
- Mixing units in one list, such as minutes and hours.
- Leaving out a zero that really happened, which inflates the mean.
- Reporting the mean of a lopsided list as if it were a typical value.
What it does not do
- Every number counts once; for marks that carry different weights, the grade calculator is the right tool.
- It does not report the mode or the standard deviation.
- It accepts up to 20 values per calculation.
Method and assumptions
The sum is every value added together. The mean is that sum divided by the number of values entered; empty rows are ignored rather than counted as zero.
For the median the values are sorted from smallest to largest. With an odd count the median is the middle one; with an even count it is the mean of the two middle values. The range is the largest value minus the smallest.
Assumptions
- Each value counts once and with equal weight.
- All values are measured in the same unit.
Edge cases
- A single value is its own mean and median, and the range is 0.
- Negative numbers are allowed and sorted below zero.
- An empty row is skipped; type 0 if a zero belongs in the list.
Sources and corrections
This calculator uses an elementary formula, so it needs no outside data source. The method, the rounding rules and how a reported error is corrected are set out in the site standards.
Result looks wrong?
Send the inputs you used and the answer you expected. Every report is checked against the formula and its tests, and confirmed errors are corrected in public.