Statistics Calculator
Descriptive statistics summarise a data set with a few numbers. Paste your values and this calculator returns the mean, median, mode, range, minimum and maximum, plus the variance and standard deviation for both a whole population and a sample.
How to use the statistics calculator
- Enter your numbers separated by commas or spaces. Decimals and negatives are fine.
- Read the averages first: the mean, the median and the mode.
- Use the spread measures (range, variance, standard deviation) to see how far values sit from the average. Use the <em>sample</em> versions when your data is only part of a larger group.
Formula
- Mean = sum ÷ count
- Median = middle value of the sorted list (average of the two middle values when the count is even)
- Mode = most frequent value
- Population variance σ² = Σ(x − mean)² ÷ n; sample variance s² = Σ(x − mean)² ÷ (n − 1)
- Standard deviation = √variance
Worked examples
Six values
For 4, 8, 6, 5, 3, 4 the sorted list is 3, 4, 4, 5, 6, 8. Mean = 30 ÷ 6 = 5. Median = (4 + 5) ÷ 2 = 4.5. Mode = 4. Range = 8 − 3 = 5. The squared deviations sum to 16, so the population variance is 16 ÷ 6 ≈ 2.667 and the sample variance is 16 ÷ 5 = 3.2, giving a sample standard deviation of about 1.789.
Choosing the right statistic
No single number describes a data set. The mean tells you the balance point, the median the middle, and the standard deviation how spread out the values are. Using them together gives an honest picture.
When mean and median disagree
Consider household incomes: a few very high earners pull the mean up while the median stays near the typical household. When the two differ a lot, the data is skewed, and the median is usually the better description of a “typical” value.
Reading standard deviation
For data shaped like a bell curve, about 68% of values lie within one standard deviation of the mean, 95% within two and 99.7% within three. A test with a mean of 70 and a standard deviation of 10 means most students scored between 60 and 80.
Population versus sample
| Population | Sample | |
|---|---|---|
| Use when | You have every value in the group | You have a subset of a larger group |
| Divide by | n | n − 1 |
Outliers
Check the minimum and maximum against the mean. A value far outside the rest may be a typing error or a genuinely unusual case. Recalculate with and without it to see how much it matters.
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- Find the mean and median of 12, 15, 11, 20, 17, 15, 9.
Show answer
Mean (average): 14.14285714 · Median: 15
- Test scores: 78, 85, 92, 66, 85, 90. Find the mean, median and mode.
Show answer
Mean (average): 82.66666667 · Median: 85
Common mistakes to avoid
- Using the mean when there are extreme outliers. One very large value pulls the mean up; the median resists it.
- Using the population formula for sample data, which understates the spread.
- Not sorting before finding the median by hand.
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the arithmetic average, the median is the middle value, and the mode is the most common value.
When should I use sample standard deviation?
When your numbers are a sample drawn from a bigger group, which is the usual case in school and research. Dividing by n − 1 corrects the bias from estimating the mean.
Can a data set have more than one mode?
Yes. If several values tie for most frequent, all are listed. If every value appears once, there is no mode.
What does standard deviation tell me?
It is the typical distance of a value from the mean. A small value means the data is tightly clustered.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.