Free statistics calculators, every step shown

Statistics Calculator

Paste a list of numbers to get the mean, median, mode, standard deviation, variance, standard error, coefficient of variation and quartiles.

The statistics calculator is a free stats calculator and statistical calculator that takes a list of numbers and returns its main descriptive statistics in one place: count, sum, mean, median, mode, range, standard deviation, standard error, coefficient of variation and absolute deviations. You type or paste the numbers, and the results update as you type. The maths runs in your browser, there is no account or sign-up, and nothing you enter is uploaded. Use it for a quick, checkable summary of a data set for a report, a class, a quality check or a cross-check against a spreadsheet. It accepts up to 50,000 values and shows the formulas with your numbers substituted, so you can see how each result was reached.
Statistics calculator example

How to use the Statistics calculator

  1. Click into the number box and type or paste your values. Separate them with commas, spaces, semicolons or new lines.
  2. Read the summary: count, sum, mean, median, mode(s), minimum, maximum and range.
  3. Find the standard deviation and variance. Both the sample and population versions are listed; under “Treat the numbers as”, choose a sample or the whole population for the headline result.
  4. Check the coefficient of variation, the standard error and the two absolute deviations, which are labelled separately.
  5. Look at the table of sorted values (position, rank, z-score) and the dot plot of mean, median and ±1 standard deviation.
  6. Read any warning. Warnings appear for a single value, identical values, fewer than 8 values, and a coefficient of variation with negative data.
  7. Open “How it was calculated” under the result to see the formula, the values substituted and the answer with units.
  8. Open “More options” for the less common inputs. Choose a quartile method there if you need Q1, Q3 and the IQR calculated another way.

To start from a worked case, press a preset button above the form. Press “Reset” to return to the starting example. “Copy result” copies the result lines with a link. “Copy link” copies the page address, which stores every input in the ?s= part of the URL, so the same calculation reopens later or can be sent to a colleague. “Print / save as PDF” produces a one-page record with the inputs, results, calculation steps and date.

What is a statistics calculator and what does it give me?

A statistics calculator reads a list of numbers and summarises it with standard measures. It tells you how many values there are, where the centre lies, how spread out they are, and how precisely the mean is estimated.

The sum of squared deviations, Σ(x − x̄)², and the raw sum of squares, Σx², are both given. The first feeds the standard deviation, and the second is used in some textbook formulas.

How do I find the mean, median and mode of a data set?

Add all the values and divide by n to get the mean. Sort the values and take the middle one as the median. If n is even, the median is the average of the two middle values. The mode is the value that appears most often.

Take the data 12, 15, 11, 18, 14, 15, 13, 16, 15, 20. The sum is 149, so the mean is 149 ÷ 10 = 14.9. Sorted, the values are 11, 12, 13, 14, 15, 15, 15, 16, 18, 20. The two middle values are both 15, so the median is 15. The value 15 appears three times, so the mode is 15. A data set can have more than one mode, and the calculator lists all of them. The range is 20 − 11 = 9.

How do I calculate standard deviation from a list of numbers (sample or population)?

Standard deviation measures the typical distance of values from the mean. Square the differences from the mean, average them, then take the square root. Use n − 1 for a sample and n for a population.

  1. Find the mean.
  2. Subtract the mean from each value and square the result.
  3. Add the squared differences.
  4. Divide by n − 1 (sample) or n (population).
  5. Take the square root.

Use the sample version when your numbers are a subset of a larger group. Use the population version when the list is the whole group. For the example above, the sample standard deviation is 2.6854 and the population standard deviation is 2.5475. For 2, 4, 4, 4, 5, 5, 7, 9 treated as a population, the mean is 5 and the standard deviation is exactly 2.

How do I calculate the coefficient of variation?

The coefficient of variation (CV) is the standard deviation divided by the absolute mean, multiplied by 100 percent. It expresses spread relative to the size of the values, so you can compare variability between data sets with different units or scales.

For the example above, using the sample standard deviation, the CV is 2.6854 ÷ 14.9 × 100 = 18.02 %. For the population of 2, 4, 4, 4, 5, 5, 7, 9, the CV is 2 ÷ 5 × 100 = 40 %. The CV becomes hard to interpret when the data contain negative values, which is why the calculator warns you in that case.

What is the standard error of the mean and how is it calculated?

The standard error of the mean (SE) is the standard deviation divided by the square root of n. It estimates how much the sample mean would vary from sample to sample, so it describes the precision of the mean rather than the spread of the data.

For the example, SE = 2.6854 ÷ √10 = 0.84918. To turn a standard error into a range of plausible values for the mean, use the confidence interval calculator.

Which MAD does this calculator use — mean absolute deviation or median absolute deviation?

It gives both, and labels them separately. The mean absolute deviation is the average of the absolute differences from the mean. The median absolute deviation is the median of the absolute differences from the median.

For the example, the mean absolute deviation is 1.92 and the median absolute deviation is 1.5. The median absolute deviation is also shown multiplied by 1.4826, which makes it an estimate of σ for normally distributed data. Because it depends on the median, it is less affected by outliers than the mean-based version.

Sources

Worked examples

InputResult
10 values from 11 to 20mean 14.9, standard deviation 2.685, median 15
8 values from 2 to 9mean 5, standard deviation 2, median 4.5
12 values from 64 to 95mean 83.33, standard deviation 9.461, median 86.5
10 values from 10.1 to 10.5mean 10.29, standard deviation 0.1197, median 10.3
15 values from 1 to 9mean 5.133, standard deviation 2.825, median 5

Calculated by the tool above with these values.

Frequently asked questions

Can I use the results in commercial projects or client reports?

Yes. Results may be used in any work, including commercial reports, theses and client projects, without attribution.

Is the calculator free, and is anything I type uploaded?

The calculator is free and has no account or sign-up. Everything is calculated in your browser, and nothing you type is uploaded.

Can I print or share a calculation?

Yes. “Print / save as PDF” produces a one-page record with the inputs, results, calculation steps and date. “Copy link” stores every input in the URL, so anyone with the link can reopen the same calculation.

Why does the calculator show two standard deviations?

It shows the sample and population versions every time, because they answer different questions. A setting chooses which one is the headline result. Use the sample version when your data is a sample from a larger group.

What does the warning about fewer than 8 values mean?

With very few values, the skewness and kurtosis estimates and the quartiles are unstable, so the calculator warns you. The basic results like the mean and standard deviation are still correct for the numbers you entered.

Why does the calculator warn about a coefficient of variation with negative data?

The CV divides by the absolute mean, so it can give a misleading picture when values are negative or the mean is close to zero. Check whether a relative measure is meaningful for your data before you use it.

Will the quartiles match the box plot calculator?

Yes. Both tools use the same quartile method, so they give identical Q1 and Q3 for the same numbers, provided you choose the same method.