Statistics Calculator (Mean, Median, Variance, Standard Deviation, Quartiles)

Paste a list of numbers separated by commas, spaces, or line breaks to instantly get the mean, median, mode, range, variance and standard deviation (both population and sample), quartiles (Q1-Q3), a frequency table, and a histogram.

Last updated: 2026-09-05

What this statistics calculator produces

Paste a set of numbers and this tool works out the descriptive statistics in one pass: the count (n), sum, mean, median, mode, minimum, maximum and range, plus variance and standard deviation given for both the population and the sample definition. Showing both side by side means you can compare them when you are unsure which one your data calls for.

There are two ways to compute variance: dividing by n gives the population variance, dividing by n−1 gives the sample variance, also called the unbiased estimate. Use the population figure if your data covers everything you are studying, and the sample figure if it is a subset drawn from a larger group. Quartiles (Q1 to Q3), the interquartile range and a frequency table with a histogram are produced at the same time.

How to use the calculator

Enter your numbers Separate values with commas, spaces or line breaks. A mixture of separators is recognised without any extra work.
Paste straight from a spreadsheet Copy a column from Excel or Google Sheets and paste it in; the line breaks are treated as separators and only the numbers are picked out.
Read the results Mean, median, mode, variance, standard deviation and quartiles are recalculated as you type, with no button to press.
Study the shape with the histogram The frequency table and histogram show how many values fall into each class, which makes skew and the position of the peak visible at a glance.

Tips for getting more out of it

You can separate values with commas, spaces, or line breaks in any combination — pasting a column straight from a spreadsheet is recognized correctly too.
Sample standard deviation (the unbiased variance divided by n − 1) is used when your data is a sample drawn from a larger population rather than the whole population itself. If you have data for every member of the population, use the population variance instead.
The interquartile range (IQR) is far less sensitive to outliers than the mean or the range, making it a more robust measure of spread for messy real-world data.
If multiple values tie for the highest frequency, all of them are shown as the mode. If every value occurs exactly once, the result shows "no mode."
The number of histogram bins is chosen automatically with Sturges' formula (based on the sample size), so larger datasets get finer-grained bins.

When this calculator is useful

Analysing test scores

Paste a whole class’s marks and the mean, median and standard deviation tell you quickly how widely results are spread and how the stronger candidates sit.

Summarising quality control data

Enter measurements from a production line and check, from the mean and standard deviation, whether variation is still within tolerance.

Summarising survey answers

For five-point scales and similar, the mean and the mode show where responses have concentrated.

Drafting statistics for coursework

The basic figures a report needs, quartiles included, are produced without any hand calculation, ready to be written up.

Terms used in descriptive statistics

Mean: The sum of all values divided by how many there are. It describes the centre of the data but is easily pulled by outliers.
Median: The value sitting exactly in the middle once the data is sorted. With an even count, the mean of the middle two values is used.
Mode: The value that occurs most often. Where several values tie, all of them are shown; where every value occurs equally often, the result is reported as none.
Population variance: Assumes the data is the entire group under study. The squared differences from the mean are summed and divided by n.
Sample variance (unbiased variance): Assumes the data is a sample drawn from a larger population. The squared differences are divided by n−1 instead, and at least two values are needed.
Standard deviation: The square root of the variance. Because it returns the figure to the original units, it makes the size of the spread far easier to judge intuitively.
Quartiles: The values that cut the sorted data into four equal parts. This tool splits the data at the median and takes the median of each half as Q1 and Q3.
Interquartile range (IQR): Q3 minus Q1. Because it ignores the extremes, it describes the spread of the data without being distorted by outliers.

Frequently Asked Questions

Variance measures spread as the average of the squared differences from the mean. Standard deviation is the square root of variance, which brings it back to the same units as the original data, making it easier to interpret and compare intuitively.

Use population variance if your data covers every member of the group you care about. Use sample variance (dividing by n − 1, the unbiased estimator) if your data is only a sample drawn from a larger population — this is the common case for surveys, test scores, and most real-world datasets.

Yes. Several conventions exist for defining quartiles, and different statistical software can give slightly different results. This tool splits the sorted data into a lower half and an upper half at the median (excluding the median itself for an odd count) and takes the median of each half as Q1 and Q3.

The mode is the value (or values) that occur most often. If two or more values tie for the highest frequency, all of them are reported as the mode. If every value occurs exactly once, there is no meaningful mode, so the tool reports "none."

The mean and the range are heavily influenced by outliers, so for data that includes extreme values, checking the median and the interquartile range (IQR) alongside them gives a more accurate picture of the overall distribution.

Side Note — When was the term "standard deviation" coined?

The statistician Karl Pearson is credited with coining the term "standard deviation" in an 1893 paper, giving a single name to a concept — essentially the square root of a mean squared error — that had previously been referred to inconsistently. Pearson was one of the founders of modern descriptive statistics, and his name also lives on in the Pearson correlation coefficient and the chi-squared test.

Whether to divide the sum of squared deviations by n or by n − 1 is a key question for understanding the difference between a "sample" and a "population" in statistics. Because computing variance from a sample mean tends to slightly underestimate the true population variance (a loss of one degree of freedom), dividing by n − 1 instead yields an unbiased estimator when inferring a population's spread from a sample. This correction is attributed to Ronald Fisher, whose work profoundly shaped statistics in the early 20th century.

Quartiles and the box plot were popularized by the American statistician John Tukey. In the 1970s he championed "exploratory data analysis," an approach that emphasizes getting a rough, hands-on feel for the shape of data before reaching for complex formulas. Box plots remain a go-to tool for visualizing outliers today.

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