Average Calculator
Enter numbers separated by commas, spaces or new lines.
About this calculator
Paste or type a list of numbers, separated by commas, spaces or new lines, and the Average Calculator returns the mean, median, mode, range, count, sum, minimum, maximum, variance and standard deviation in one go.
It labels the standard deviation as population, which divides by n, and also shows the sample standard deviation, which divides by n ā 1. Use the sample version when your numbers are a sample drawn from a larger group.
How to use it
- Type or paste the numbers. The default list is a sample you can overwrite.
- The results update as you type.
- Read the mean, median, mode and spread.
Definitions
Mean = Sum Ć· Count. The median is the middle value of the sorted list, or the mean of the two middle values. The mode is the most frequent value, and "None" is shown when every value occurs once. Range = Max ā Min. Population variance = Ī£(x ā mean)Ā² Ć· n and sample variance = Ī£(x ā mean)Ā² Ć· (n ā 1). Standard deviation is the square root of the variance.
Worked example
Data: 12, 45, 7, 89, 34, 56, 23
| Sum / Count | 266 / 7 |
| Mean | 38.0000 |
| Median | 34 |
| Mode | None |
| Range | 82 |
| Population standard deviation | 26.3276 |
| Sample standard deviation | 28.4371 |
Tips and common mistakes
- The median is a better 'typical' value than the mean when there are outliers.
- Use the sample standard deviation for exam or survey data, which are samples.
- Check for typos: one extra zero can distort the mean.
- A weighted average needs weights; this tool treats every value equally.
- Average marks across subjects with different weightage should be weighted by credits.
Frequently asked questions
How do I calculate an average?
Add all values and divide by how many there are.
What is the difference between mean, median and mode?
Mean is the arithmetic average, median the middle value and mode the most frequent value.
Which standard deviation should I use?
Use sample (n ā 1) for a sample of a larger group and population (n) when you have everyone.
What if there is no mode?
The tool shows None when all values are unique.
Can I paste numbers from Excel?
Yes, new lines and spaces are accepted as separators.
What is the range?
The difference between the largest and smallest value.