Calculate mean, median, mode, standard deviation, variance, and more from a dataset. Ideal for students and data analysts.
Enter numbers separated by commas
Enter values above to see results
Mean = Σx / n | σ = √(Σ(x − μ)² / n)ΣxSum of all valuesnNumber of valuesμPopulation meanσPopulation standard deviationDescriptive statistics summarize a dataset with a few key numbers. The mean is the arithmetic average. The median is the middle value when sorted. The mode is the most frequent value. Standard deviation measures how spread out the values are from the mean.
Statistics is the science of collecting, analyzing, interpreting, and presenting data. Descriptive statistics - the branch this calculator addresses - summarizes and describes the main features of a dataset. From academic research to business analytics, sports performance analysis to medical studies, statistical measures are the language of data-driven decision making.
Enter your dataset as comma-separated numbers. The calculator instantly computes eight key statistical measures: mean, median, mode, standard deviation, variance, range, count, and sum. Each result is accompanied by a step-by-step calculation showing the methodology.
| Measure | Formula |
|---|---|
| Mean | Σx / n |
| Median | Middle value of sorted data (avg. of two middle values if n is even) |
| Mode | Most frequently occurring value(s) |
| Range | Max value − Min value |
| Population variance (σ²) | Σ(x − μ)² / n |
| Population std. deviation (σ) | √(Σ(x − μ)² / n) |
A small five-value dataset, computing the core descriptive statistics.
Mean 4.8, median 4, mode 4, standard deviation ≈ 2.04, range 6.
Here the mean sits above the median because the value 8 pulls the average up — a small hint of right skew.
This calculator handles datasets of any size, automatically sorts the data for median calculation, identifies all modes in multimodal datasets, and provides both variance and standard deviation. It is suitable for students learning statistics and professionals needing quick descriptive analysis.
Ensure your numbers are separated by commas without extra spaces or special characters. A common conceptual mistake is using standard deviation when variance is required (or vice versa) in formulas - always check which measure a formula expects.
Calculate percentages, percentage change, and percentage of a number instantly with step-by-step explanations.
Solve quadratic equations ax² + bx + c = 0 using the quadratic formula. Find real and complex roots with full working.