Statistics Calculator

The mean is the arithmetic average, so it uses every value and can move sharply when a few points are extreme. The median is the middle of the sorted list (or the average of the two middle values), so it resists outliers and better reflects a “typical” value when data is skewed. If your dataset has occasional spikes, heavy tails, or measurement glitches, the median is often more stable. If your data is roughly symmetric without major outliers, the mean is efficient and pairs naturally with standard deviation for spread.

Use population standard deviation when your numbers represent the entire group you care about (for example, all items produced in a specific batch). Use sample standard deviation when your values are a subset used to estimate a broader process (for example, a small inspection sample from a continuous production line). Sample variance divides by n − 1 to reduce bias in the estimate. If you are unsure, sample is a safer default for inference and comparison, while population is appropriate for complete enumerations of a fixed group.

Mode is defined as the value (or values) that occur most frequently. If two or more values share the same highest frequency, the dataset is multimodal. This calculator reports all tied modes as a list rather than forcing a single answer. If every value appears exactly once, there is no mode in the usual descriptive sense, so the calculator shows “No mode.” For measurement data, multimodality can hint at mixed populations (for example, two operating states), so it’s often worth checking the raw values or grouping by conditions.

This calculator uses the Tukey “median-of-halves” method. First it sorts the data and finds the median (Q2). For odd n, the median is excluded from both halves; for even n, the data splits evenly. Q1 is the median of the lower half, and Q3 is the median of the upper half. Quartiles can vary slightly across software because there are multiple accepted conventions, especially for small datasets. Stating the method makes your results reproducible and easier to compare across reports and tools.

Yes—decimals and negative values are supported, including formats like -3, 4.25, and .5. The parser uses strict numeric validation to avoid accidental misreads, and it rejects NaN and Infinity. Tokens are split on commas, spaces, tabs, new lines, and semicolons, then trimmed. If “Ignore non-numeric tokens” is off, the calculator blocks the run and shows a short list of invalid examples so you can clean your input. If it’s on, invalid tokens are skipped and the stats use only valid numbers.

Start by deciding what counts as a valid measurement: remove units, labels, and placeholders like “n/a.” Check for impossible values (for example, negative lengths) and confirm whether those represent real cases or entry errors. If values were recorded with different rounding, keep enough precision to avoid artificial ties. For outlier handling, don’t delete extremes by default—compare mean/SD with median/IQR to understand their influence, then document any rule you apply (such as winsorizing or excluding values beyond a known physical limit).

Standard deviation describes how far values typically deviate from the mean, in the same units as the data. When data is roughly bell-shaped, many observations fall within about one SD of the mean, and larger SD means more variability. IQR focuses on the middle half of the data: it is Q3 − Q1, so it ignores the lowest 25% and highest 25%. That makes IQR robust when outliers exist. If SD is high but IQR is modest, you likely have a few extremes; if both are high, the spread is broad throughout.

Your dataset is processed locally in your browser; the calculator does not transmit values to a server. The precision selector changes how numbers are displayed (rounded to your chosen decimals), while the underlying calculations keep higher internal precision to reduce rounding error. For reporting, choose a precision that matches your measurement resolution and audience. If you need to compare close groups, increase precision to avoid hiding small differences in mean or SD. Copy outputs are plain text so you can paste them directly into notes, emails, or documents.