Check a numeric dataset with explicit sample, population, quartile and skewness conventions. Invalid entries are identified instead of silently discarded.
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This statistics calculator provides a comprehensive set of descriptive statistics for any dataset you enter. Whether you're a student working on a statistics assignment, a researcher analyzing survey data, or a professional making data-driven decisions, this tool gives you instant results without needing spreadsheet software or statistical packages.
Descriptive statistics summarize and describe the main features of a dataset. The measures of central tendency — mean, median, and mode — tell you where the "center" of your data lies. The mean is the arithmetic average, the median is the middle value (resistant to outliers), and the mode is the most frequent value. For skewed data, the median is often more representative than the mean.
Measures of dispersion — standard deviation, variance, range, and interquartile range (IQR) — tell you how spread out your data is. A low standard deviation means values are clustered close to the mean, while a high standard deviation indicates wide spread. The coefficient of variation (CV) expresses sample standard deviation relative to the absolute mean. It is most useful for ratio-scale measurements with a meaningful zero and non-zero mean; it is not a universal quality score.
Quartiles divide your sorted data into four equal parts. Q1 (25th percentile) marks the lower quarter, Q2 (50th percentile) is the median, and Q3 (75th percentile) marks the upper quarter. The IQR (Q3 - Q1) represents the middle 50% of your data and is commonly used to identify outliers — values more than 1.5 times the IQR below Q1 or above Q3.
Skewness measures the asymmetry of the distribution. Positive skewness indicates a right tail (common in income data), while negative skewness indicates a left tail. Understanding skewness helps you choose appropriate statistical methods and interpret your data correctly.
Population SD divides by N (total count), while sample SD divides by N-1 (Bessel's correction). Use sample SD when your data is a subset of a larger population. This calculator provides both values.
Use the median when your data is skewed or contains outliers. For example, salary data is typically right-skewed (a few very high earners pull the mean up), so the median salary better represents the "typical" worker. If your data is roughly symmetric, mean and median will be similar.
It uses inclusive linear interpolation at position (n − 1) × q. Other software and textbooks may use a different convention, so check the method required by your assignment or analysis.
CV is most useful for ratio-scale measurements with a meaningful zero and a non-zero mean. There is no universal percentage that makes every dataset “high variability”, and comparing unrelated units can be misleading.
Updated for 2026. Here is exactly how each statistic is produced, the assumptions behind it, and what to verify before you rely on it.
QUARTILE.INC/SKEW or other calculators. Verify that your dataset is complete, numeric, and in a single consistent unit, and decide separately how to treat outliers before drawing conclusions.