Calculate mean, median, mode, range, and standard deviation instantly. Paste any dataset. Free statistics calculator. No signup required.
Statistical calculations should take seconds — not minutes of manual formula entry in Excel. Paste any dataset of numbers and our calculator instantly computes mean, median, mode, range, variance, standard deviation, and percentiles. Perfect for data analysis, academic work, business reporting, and scientific research.
Mean (average): sum of all values divided by count. Sensitive to outliers — one extreme value dramatically shifts the mean. Median: middle value when sorted in order. Resistant to outliers — better measure for skewed data. Real example: average US household income (mean $105,000) versus median household income ($74,000) — the gap shows income inequality pulling mean upward. Median is usually more representative for real-world financial data.
Standard deviation measures spread around the mean. Low SD: data points are clustered close to the mean (consistent results). High SD: data points are spread widely (variable results). Practical applications: Test scores: SD of 5 means most students scored within 5 points of average. Investment returns: high SD = volatile investment, low SD = stable investment. Manufacturing quality: low SD = consistent production. The 68-95-99.7 rule: 68% of data within 1 SD, 95% within 2 SD, 99.7% within 3 SD of the mean.
Standard deviation steps: Step 1: Calculate the mean. Step 2: Subtract mean from each data point. Step 3: Square each difference. Step 4: Sum all squared differences. Step 5: Divide by n-1 (for sample SD) or n (for population SD). Step 6: Take the square root. Example: dataset 2, 4, 4, 4, 5, 5, 7, 9. Mean = 5. SD = 2. Most Excel users use STDEV() function — our calculator does this instantly with paste-and-go.
Population SD (σ): use when you have all data for the entire population. Divides by n. Sample SD (s): use when your data is a sample from a larger population. Divides by n-1 (Bessel's correction). In practice: most data analysis uses sample SD because you almost never have the complete population. In Excel: STDEV() = sample SD, STDEVP() = population SD.
Context determines what is good. For test scores: SD of 10-15 on 100-point test shows healthy distribution. For manufacturing: lower is always better — Six Sigma targets 3.4 defects per million (6 SD from mean). For investment returns: depends on your risk tolerance — S&P 500 annual SD is approximately 15-17%. Lower SD means more predictable outcomes — whether that is good depends entirely on your context.
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The Free Statistics Calculator — Mean, Median, Mode, and Standard Deviation uses the same formulas, rates, and reference data that financial planners, professionals, and government sources publish. Results are estimates intended for planning and education — for situations involving large sums or legal consequences, confirm with a qualified professional before acting.
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