Why use Average Calculator
Enter a list of numbers and the calculator returns ten figures: count, sum, mean, median, mode, range, minimum, maximum, population standard deviation and variance, followed by the values sorted from smallest to largest. For 12, 15, 9, 22, 15, 18, 7 the mean is 14, the median is 15, the mode is 15 and the range is 15. Numbers can be separated by commas, spaces, semicolons or line breaks, so a column copied from a spreadsheet works as pasted. Negative numbers and decimals with a point are accepted. Results are rounded to two decimal places.
Worked examples: mean, median, mode and range for real lists
Each result below is what the calculator returns for the list shown.
Odd count with one mode
12, 15, 9, 22, 15, 18, 7
Count 7, sum 98, mean 14, median 15, mode 15, range 15, minimum 7, maximum 22, standard deviation 4.78, variance 22.86. Sorted: 7, 9, 12, 15, 15, 18, 22.
Test scores with no mode
85, 92, 78, 90, 88
Count 5, sum 433, mean 86.6, median 88, mode None, range 14, standard deviation 4.88, variance 23.84.
Even count, median between two values
4, 8, 15, 16, 23, 42
Count 6, sum 108, mean 18, median 15.5, mode None, range 38, standard deviation 12.32, variance 151.67.
Two modes
10, 2, 38, 23, 38, 23, 21
Count 7, sum 155, mean 22.14, median 23, mode 38, 23, range 36, standard deviation 12.3, variance 151.27.
Tied modes are listed in the order they first appear in your input, not in numerical order.
Salaries with one outlier
30000 32000 35000 38000 41000 250000
Count 6, sum 426,000, mean 71,000, median 36,500, mode None, range 220,000, standard deviation 80,133.22.
Five of the six salaries are below 42,000, yet the mean is 71,000. The median of 36,500 is the honest summary.
Negative numbers
-5, 0, 5, 10
Count 4, sum 10, mean 2.5, median 2.5, mode None, range 15, minimum -5, maximum 10, standard deviation 5.59, variance 31.25.
The range crosses zero: 10 minus -5 is 15.
What each statistic means and how it is calculated
| Statistic | Rule | For 2, 4, 4, 4, 5, 5, 7, 9 |
|---|---|---|
| Count | How many values are in the list | 8 |
| Sum | All values added together | 40 |
| Mean | Sum divided by count | 5 |
| Median | Middle value of the sorted list, or the average of the two middle values | 4.5 |
| Mode | Value or values that occur most often | 4 |
| Range | Maximum minus minimum | 7 |
| Minimum | Smallest value | 2 |
| Maximum | Largest value | 9 |
| Variance | Average of the squared differences from the mean | 4 |
| Std deviation | Square root of the variance | 2 |
Variance and standard deviation use the population formula, dividing by the count n.
Formulas for mean, median, range and standard deviation
Mean = sum of values / n. Median = value at position (n + 1) / 2 in the sorted list when n is odd, or the average of the values at positions n / 2 and n / 2 + 1 when n is even. Range = maximum - minimum. Variance = sum of (value - mean) squared / n. Standard deviation = square root of variance.
Here n is the number of values. Take 12, 15, 9, 22, 15, 18, 7. The sum is 98 and n is 7, so the mean is 98 / 7 = 14. Sorted, the list is 7, 9, 12, 15, 15, 18, 22 and position (7 + 1) / 2 = 4 holds 15, the median. The range is 22 - 7 = 15. The squared differences from 14 are 4, 1, 25, 64, 1, 16 and 49, which add up to 160. Dividing by 7 gives a variance of 22.86, and its square root is the standard deviation, 4.78.
Population or sample: which standard deviation this is
The calculator reports the population standard deviation and population variance. It divides the sum of squared differences by n, the number of values. That is the right figure when your list is the whole group you care about: every score in one class, every reading taken in one month.
If your list is a sample drawn from a larger group and you want to estimate the spread of that larger group, the usual formula divides by n - 1 instead. This tool does not output that sample figure. You can get it from the population variance shown here: multiply by n and divide by n - 1, then take the square root. For 12, 15, 9, 22, 15, 18, 7 the population variance is 160 / 7 = 22.86, the sample variance is 160 / 6 = 26.67, and the sample standard deviation is about 5.16.
The mean and the median do not have separate versions. The sample mean and the sample median are calculated exactly like the mean and median of any list, so the Mean and Median figures here apply either way.
Input formats that work and ones that do not
- Commas, spaces, semicolons and line breaks all separate values, and you can mix them in one list.
- Negative numbers and decimals written with a point, such as -5 or 7.25, are accepted.
- Do not use thousands separators. 1,000 is read as two values, 1 and 0. Type 1000 instead.
- Do not use a decimal comma. 1,5 is read as 1 and 5. Type 1.5 instead.
- Scientific notation such as 1e3 is read as 1,000.
- Anything that is not a number, such as a currency symbol, a unit or a time like 23:45, stops the calculation and the tool names the entry it could not read.
- There is one value per entry. The tool has no weights or frequency column, so repeat a value as many times as it occurs.
How to get your result
- 1
Type or paste your values into the Numbers box, separated by commas, spaces, semicolons or new lines.
- 2
Read Mean, Median, Mode and Range in the Statistics panel, alongside Count, Sum, Minimum and Maximum.
- 3
Check Std deviation and Variance if you need a measure of spread. Both are population figures.
- 4
Use Sorted values to see the list in ascending order, and copy it if you need the ordered data elsewhere.