Descriptive Statistics Calculator

Every core descriptive statistic — mean, median, mode, spread and shape — on one page

Paste your data below for the complete set of descriptive statistics at once — measures of center (mean, median, mode), spread (standard deviation, variance, IQR, range) and position (quartiles, percentiles) — with a full step-by-step solution.

Enter Your Data Points

Textbooks differ — pick the method yours uses.

Results

Mean15.1818
Std deviation (sample)11.1698
Variance (sample)124.7636

Five Number Summary

Minimum4
Q1 (25th)8
Median15
Q3 (75th)23
Maximum42
Interquartile range (IQR)15
Count (n)11
Outliers (1.5 × IQR rule)None

Additional Statistics

Mean (average)15.1818
Mode8
Range38
Sum167
Std deviation (sample)11.1698
Std deviation (population)10.65
Variance (sample)124.7636
Mean absolute deviation8.0165
Coefficient of variation0.7357
Standard error of the mean3.3678
10th percentile4
90th percentile23
Lower inner fence (Q1 − 1.5·IQR)-14.5
Upper inner fence (Q3 + 1.5·IQR)45.5

Box & Whisker Plot

Histogram

Step-by-step solution

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What are descriptive statistics?

Descriptive statistics summarize a dataset's center, spread, and shape without making inferences beyond the data itself (that's the job of inferential statistics, like the t-test or confidence interval calculators). They're the first thing you compute when looking at any new dataset.

The three families of descriptive statistics

Measures of central tendency — mean, median and mode — describe where the "middle" of the data sits. Measures of spread — standard deviation, variance, range and IQR — describe how tightly or loosely the values cluster. Measures of position — quartiles and percentiles — describe where a specific value falls relative to the rest of the data.

Which statistics should you report?

For roughly symmetric data without extreme outliers, the mean and standard deviation are the standard pair to report. For skewed data or data with outliers, the median and IQR are more robust, since a single extreme value can distort the mean and standard deviation but barely moves the median or quartiles. This calculator reports both families side by side so you can compare them for your specific dataset — the "Five Number Summary" and "Additional Statistics" panels below cover the position/spread and center/shape statistics respectively.

How this page differs from the other calculators on this site

Every calculator on this site computes the full statistic bundle under the hood — this page is simply the one built to show all of it at once, rather than spotlighting a single statistic like standard deviation or IQR. If you know exactly which single statistic you need, the dedicated calculators (linked below) show worked steps specific to that statistic.

Frequently asked questions

What is the difference between descriptive and inferential statistics?

Descriptive statistics (this page) summarize the data you actually have. Inferential statistics — like the t-test or confidence interval calculators on this site — use that data to draw conclusions about a wider population.

Should I use the sample or population standard deviation?

Use the sample version (dividing by n−1) when your data is a sample drawn from a larger population, which is the common case. Use the population version (dividing by n) only when your data represents the entire group you care about.

Why does this calculator show three quartile methods?

Textbooks disagree on how to compute Q1 and Q3 when the median falls between two values. This calculator supports Tukey (exclusive), Moore & McCabe (inclusive) and linear interpolation (the Excel convention) so the result matches whichever method your course or software uses.

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