Free Statistics Calculator
Compute mean, median, mode, variance, standard deviation, range, min, and max for any dataset. Enter numbers separated by commas or new lines. Instant results with full descriptive statistics. Free, private — all calculations run in your browser.
Interpretation Guide
- Mean (7.3333) > Median (5.0000) — right-skewed distribution. High values pull the mean up.
- No outliers detected using the 1.5×IQR rule (Tukey fences).
- Coefficient of variation = 69.86%. High relative spread — data is highly variable.
About This Statistics Calculator
The Statistics Calculator computes the full suite of descriptive statistics for any dataset you enter. Descriptive statistics summarise the key properties of a collection of data — where it is centred, how spread out it is, and its extreme values — without making inferences about any larger population. They are the foundation of data analysis in every field: science, business, social research, healthcare, and engineering.
The Formulas — How Each Statistic Is Computed
Median = middle value of sorted data (avg of two middle values if n is even)
Mode = most frequently occurring value(s)
Variance = Σ(x − μ)² / n
Std Dev = √Variance
Range = max − min
Where Σ denotes summation over all n values, μ is the population mean, and n is the count of values. The variance and standard deviation shown are population statistics (dividing by n). To get sample statistics, divide the sum of squared deviations by n − 1 instead.
Descriptive vs. Inferential Statistics
Descriptive statistics describe the data you have — they make no claims about any broader population. The mean exam score of your class of 30 students is a descriptive statistic. Inferential statistics use a sample to draw conclusions about a larger population, and require techniques such as hypothesis testing, confidence intervals, and regression analysis. This calculator covers descriptive statistics. For inferential analysis, see our Z-Score Calculator and Confidence Interval Calculator.
When to Use Mean vs. Median
The mean is the most familiar measure of centre, but it is sensitive to extreme values (outliers). A single very large or very small value pulls the mean away from the typical value. The median — the middle value in sorted order — is resistant to outliers and is therefore preferred for skewed data. For example, US household income is always reported as median income, because a small number of very high earners would make the mean misleadingly high. As a rule: if the mean and median differ substantially, the distribution is skewed and the median is the more informative centre measure.
Standard Deviation and What It Tells You
Standard deviation (SD) is the most widely used measure of spread. It expresses, on average, how far values lie from the mean. For a normal (bell-shaped) distribution: approximately 68% of values fall within ±1 SD of the mean, 95% within ±2 SD, and 99.7% within ±3 SD (the empirical rule). A low SD means values cluster tightly around the mean; a high SD means values are spread widely. Always report SD alongside the mean — mean without SD gives an incomplete picture of any dataset.
Privacy Notice
All calculations run entirely in your browser. No data you enter is transmitted to any server, stored in any database, or shared with third parties. Your dataset stays completely private on your device. See our Privacy Policy for full details.
When to Use This Calculator
Summarise experimental results — means, standard deviations, and ranges — for inclusion in a lab report, thesis, or research paper.
Calculate average transaction values, standard deviation of sales, or range of customer wait times to support KPI dashboards and management reports.
Monitor manufacturing measurements. Compare the mean and SD of part dimensions against specification tolerances to catch processes drifting out of control.
Analyse Likert-scale survey responses: compute the mean rating, SD (spread of opinion), and mode (most common response) across respondents.
Report trial results with the mean ± standard deviation format. Identify the range and any potential measurement errors or anomalies in experimental data.
💡 Pro Tips
Always report the mean and standard deviation together — the mean alone tells you where the data is centred, but the SD tells you how spread out it is. A mean of 50 with SD = 2 represents a tight cluster around 50; a mean of 50 with SD = 25 represents enormous variability. Reporting one without the other gives an incomplete picture.
Check for outliers before reporting the mean. A single extreme value can shift the mean dramatically while leaving the median nearly unchanged. A quick visual check: if mean and median differ by more than one standard deviation, suspect significant skew or outliers. Use the median for skewed data.
Bimodal distributions (two modes) signal that your dataset may contain two distinct subgroups. Before reporting a single mean or SD, investigate whether the data should be split into two groups and analysed separately. For example, heights of men and women combined create a bimodal distribution — summarising with one mean obscures the real structure.
Box plots (whisker plots) are the most efficient way to visualise the five-number summary: minimum, Q1 (25th percentile), median (Q2), Q3 (75th percentile), and maximum. Any point beyond 1.5 × IQR from Q1 or Q3 is conventionally flagged as an outlier. Pair your statistics report with a box plot for instant clarity.
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