Statistics Calculator
Adjust the inputs below. Results update as you type.
How it works
Quartiles divide sorted data into four equal parts: Q1 (25th percentile), Q2 (median, 50th), Q3 (75th). IQR = Q3−Q1; outliers > Q3+1.5×IQR or < Q1−1.5×IQR. Skewness measures distribution asymmetry (0 = symmetric). Kurtosis measures tail heaviness (3 = normal distribution). Z-score = (value − mean) / SD tells you how many standard deviations from the mean a value falls.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Core measures: mean (average), median (middle value), mode (most frequent), range (max − min), variance, and standard deviation (spread around the mean).
Worked example
For 4, 8, 6, 8, 10: mean = 7.2, median = 8, mode = 8, range = 6.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
Mean vs. median — which to use?+
The mean suits symmetric data; the median is better for skewed data or outliers, since it is not pulled by extreme values.
What does variance measure?+
The average squared distance of values from the mean. Its square root, the standard deviation, expresses spread in the original units.
What is the mode?+
The most frequently occurring value. A dataset can have one mode, several, or none if all values are unique.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.
Guided next steps
Want the full workflow? Use this calculator inside a step-by-step guide.