Statistics
Statistics Calculator: Mean, Median, Standard Deviation And More
Last updated: October 2026
Written by Jessica Hill
A statistics calculator summarizes a data set in seconds. For the numbers 2, 4, 4, 4, 5, 5, 7 and 9, it finds a mean of 5, a median of 4.5, a mode of 4, a range of 7, a population standard deviation of 2 and a sample standard deviation of about 2.14.
- Free, no sign-up
- Shows the working
- Runs on your device
This guide explains each result, when to use the sample or population version, and how to spot outliers. Every example was checked in Python.
How To Use The Statistics Calculator
The statistics calculator above has three tabs.
- Descriptive Statistics: paste numbers separated by commas, spaces or line breaks, or copy a spreadsheet column.
- Frequency Table: enter each value and how many times it appears, as with survey counts.
- Five-Number Summary and Outliers: see the quartiles, a box plot and any values far from the rest.
Measures Of Center: Mean, Median And Mode
Measures of center describe a typical value in the data. The three common ones answer slightly different questions.
| Measure | How to find it | Example (2, 4, 4, 4, 5, 5, 7, 9) |
|---|---|---|
| Mean | Add all values, divide by the count | 40 ÷ 8 = 5 |
| Median | Middle value of the sorted list (average the two middle values if the count is even) | (4 + 5) ÷ 2 = 4.5 |
| Mode | The value that appears most often | 4 (appears three times) |
Mean, Median And Mode: Which Average To Use
The mean uses every value, so one extreme number can pull it far away. The median only cares about the middle, so it resists extremes.
Add a single value of 30 to the example data. The mean jumps from 5 to 7.78, but the median only moves from 4.5 to 5. That is why home prices and incomes are usually reported as medians: a few very high values would make the mean misleading.
Use the mode for categories or repeated values, such as the most common shoe size sold. A data set can have one mode, several, or none.
Other Averages: Weighted, Geometric And Harmonic
Some data needs a different kind of average.
- Weighted mean: each value counts by its weight, such as credit hours in a grade point average. The GPA calculator is a weighted mean in action.
- Geometric mean: multiply the values and take the nth root. It suits growth rates. For the example data, it is about 4.60.
Measures Of Spread: Range, Variance And Standard Deviation
Spread shows how far the values are from each other. Two data sets can share a mean but look completely different.
- Range: max minus min. For the example, 9 − 2 = 7. Easy, but it only uses two values.
- Variance: the average squared distance from the mean. Here the squared distances add up to 32, so the population variance is 32 ÷ 8 = 4.
- Standard deviation (SD): the square root of the variance, which puts spread back in the original units. Here, √4 = 2.
A small SD means values cluster near the mean. A large SD means they are spread out. For data shaped like a bell curve, about 68% of values fall within 1 SD of the mean.
Coefficient of variation (CV) is SD ÷ mean, shown as a percent. It compares spread across data with different units or sizes. Here, 2 ÷ 5 = 40%. To express any ratio as a percent, the percentage calculator works the same way.
Sample Vs Population: Which Formula?
Use the population formulas when your data includes every member of the group you care about. Use the sample formulas when your data is a sample used to estimate a larger group.
| Measure | Population (divide by n) | Sample (divide by n − 1) |
|---|---|---|
| Variance | 32 ÷ 8 = 4 | 32 ÷ 7 ≈ 4.571 |
| Standard deviation | √4 = 2 | √4.571 ≈ 2.138 |
Dividing by n − 1 makes the sample estimate slightly larger. That corrects for the fact that a sample usually shows less spread than the full population. Most real research uses the sample version. If your class gave a test and you only care about that class, the population version fits.
Standard error (sample SD ÷ √n) measures how precise the mean is, not how spread out the data is. Here, 2.138 ÷ √8 ≈ 0.756. More data shrinks it.
In Excel, STDEV.S and VAR.S are the sample versions, and STDEV.P and VAR.P are the population versions.
Quartiles, IQR And The Five-Number Summary
Quartiles split sorted data into four equal parts. Q1 is the 25th percentile, Q2 is the median, and Q3 is the 75th percentile. The interquartile range (IQR) is Q3 − Q1, the spread of the middle half.
The five-number summary is min, Q1, median, Q3 and max. It is what a box plot draws.
Why quartile answers differ between tools. There is more than one accepted way to find quartiles, and small data sets show the difference clearly. For 2, 4, 4, 4, 5, 5, 7, 9:
| Method | Q1 | Q3 | Used by |
|---|---|---|---|
| Inclusive | 4 | 5.5 | Excel QUARTILE.INC, Google Sheets QUARTILE |
| Exclusive | 4 | 6.5 | Excel QUARTILE.EXC |
| Median of halves | 4 | 6 | Many textbooks and hand methods |
None of these is wrong. Use the method your class, textbook or software expects, and pick it in the calculator to match.
How To Spot Outliers
An outlier is a value far from the rest of the data. A common rule flags any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR.
Example: with 30 added to the data, the inclusive quartiles are Q1 = 4 and Q3 = 7, so the IQR is 3.
- Upper fence: 7 + 1.5 × 3 = 11.5.
- Lower fence: 4 − 1.5 × 3 = −0.5.
- The value 30 is above 11.5, so it is an outlier.
An outlier is a reason to look closer, not to delete. It might be a typing error, or it might be the most interesting value in the data.
Common Statistics Mistakes
| Mistake | Fix |
|---|---|
| Using population SD for a sample | Use n − 1 (STDEV.S) when the data is a sample |
| Reporting the mean for skewed data | Report the median too, or instead |
| Expecting the same quartiles from every tool | Check which quartile method is used |
| Deleting outliers without checking them | Find out why the value is extreme first |
Summary
- Mean, median and mode describe the center. The median resists outliers.
- Range, variance and standard deviation describe spread.
- Use sample formulas (n − 1) for samples and population formulas (n) for whole groups.
- Quartile methods differ, so match the one your class or software uses.
- Flag outliers with the 1.5 × IQR rule, then investigate them.
Next step: paste your data into the statistics calculator at the top of this page, or browse more tools on the Calc Solver homepage.
Frequently Asked Questions
What is the difference between descriptive and inferential statistics?
Descriptive statistics summarize the data you have, using values like the mean, median and standard deviation. Inferential statistics use a sample to draw conclusions about a larger group, with tools like confidence intervals and hypothesis tests. This calculator covers descriptive statistics, which are always the first step, since you need to understand your sample before you can make claims about the population.
Can the mean and median be the same?
Yes. In a perfectly symmetric data set, such as 1, 2, 3, 4 and 5, the mean and median are both 3. When the two are close, the data is roughly balanced. When the mean is much higher than the median, a few large values are pulling it up. When it is much lower, a few small values are pulling it down.
How many data points do I need?
You can calculate a mean from one value, but sample standard deviation needs at least two, since it divides by n − 1. For results that reliably describe a larger group, more data is better. Quartiles and outlier checks are hard to interpret with fewer than about 10 values, because a single number changes them a lot.
Why is variance in squared units?
Variance squares each distance from the mean before averaging, so its units are squared too. If the data is in inches, the variance is in square inches, which is hard to picture. That is why the standard deviation, the square root of the variance, is usually reported instead. It is in the same units as the original data.
How do I calculate statistics in Excel?
Excel has a function for each statistic. Use AVERAGE for the mean, MEDIAN, MODE.SNGL, MIN, MAX, STDEV.S or STDEV.P, VAR.S or VAR.P, and QUARTILE.INC for quartiles. For a quick summary of everything, the Data Analysis add-in has a Descriptive Statistics tool. Google Sheets uses the same function names for most of these.
Try it with your own numbers
The calculator at the top of this page uses the same formulas as the examples.