Average Calculator (Mean, Median, Mode)
Find the mean, median, mode, range and standard deviation of any list of numbers.
Your details
Commas, spaces or new lines all work
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Mean (average)
29.2500
8 values summing to 234.00
Includes your inputs, the full breakdown, and every row of the table.
Median
20.0000
Mode
15.0000
Range
82.0000
Standard deviation (sample)
26.9484
- Count
- 8
- Sum
- 234.0000
- Mean
- 29.2500
- Minimum
- 12.0000
- Maximum
- 94.0000
- Variance
- 726.2143
| Measure | Value |
|---|---|
| Minimum | 12.0000 |
| 25th percentile | 15.0000 |
| Median | 20.0000 |
| 75th percentile | 28.0000 |
| Maximum | 94.0000 |
| Interquartile range | 13.0000 |
What this means
- The mean sits well above the median, which means a few large values are pulling it upward. The median is the better summary here.
- Sample standard deviation divides by n−1 and is the right choice when your numbers are a sample of something larger. Use the population basis only when you have every member of the group.
How the average calculator (mean, median, mode) calculation works
The word average hides three different ideas. The mean adds everything up and divides, which is what most people intend, but it is easily distorted by extreme values. The median is the middle value once sorted and is immune to outliers, which is why incomes and house prices are almost always reported as medians. The mode is simply the most frequent value and is the only one of the three that works on categories rather than numbers.
Standard deviation describes spread rather than centre, and it is what tells you whether the average is meaningful at all. Two datasets can share a mean of fifty while one clusters tightly around it and the other swings between zero and a hundred. The gap between mean and median is a quick diagnostic: when they diverge substantially, the data is skewed and the mean is being pulled by a tail.
Frequently asked questions
When should I use the median instead of the mean?
Whenever the data has outliers or a long tail. Incomes are the classic example — a handful of very high earners drags the mean well above what a typical person earns, while the median stays at the genuine midpoint. If the mean and median differ substantially, that difference is itself telling you something.
What is the difference between sample and population standard deviation?
The divisor. Population divides by the number of values and is correct when you have measured every member of the group. Sample divides by one less, which corrects for the fact that a sample tends to understate the true spread. If your numbers are a subset of something larger, use the sample version.
Can a dataset have more than one mode?
Yes. If several values tie for the highest frequency, all of them are modes and the data is described as bimodal or multimodal. If nothing repeats at all, there is no mode. Multiple modes often indicate that two distinct groups have been mixed together.
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Disclaimer. This calculator is provided for general information and educational purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Results are estimates based on the inputs you provide and the assumptions described above. Confirm any figure with a qualified professional before acting on it.