Paste your numbers and instantly get mean, median, mode, standard deviation, variance, quartiles, range, skewness, and a visual distribution histogram.
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 the standard deviation as a percentage of the mean, making it useful for comparing variability between datasets with different units or scales.
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.
A CV above 30% is generally considered high variability. It means the standard deviation is large relative to the mean. CV is useful for comparing variability between datasets with different scales — for example, comparing the variability of heights (in cm) vs weights (in kg).