Calculate mean, median, mode, standard deviation, variance, quartiles & more from any dataset. Live histogram and box plot included.
A complete descriptive statistics calculator that computes mean, median, mode, range, sample and population variance, sample and population standard deviation, quartiles (Q1, Q3, IQR), sum of squares, geometric mean, harmonic mean, and coefficient of variation from any list of numbers. Paste data separated by commas, spaces, or newlines and get instant results plus a live histogram and box plot. Outliers flagged automatically using the 1.5×IQR rule.
The mean (arithmetic average) is the sum of all values divided by the count — it is sensitive to outliers. The median is the middle value when the data is sorted; it is robust against outliers and skewed distributions. The mode is the most frequently occurring value; datasets can be unimodal, bimodal, or multimodal. For skewed data, the median is usually a better representative than the mean. The geometric mean is preferred for growth rates and the harmonic mean for averaging rates.
Range (max − min) is the simplest spread measure but very sensitive to outliers. Variance is the average squared deviation from the mean — population variance divides by n, sample variance by (n−1) using Bessel correction. Standard deviation is the square root of variance and shares the units of the original data: roughly 68% of normally-distributed data lies within 1 SD of the mean, 95% within 2 SD. The interquartile range (IQR = Q3 − Q1) describes the spread of the middle 50% and powers outlier detection.
The 1.5×IQR rule is the most common outlier test: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are flagged. The coefficient of variation (CV = SD/|mean| × 100%) lets you compare variability across datasets with different units or scales — a CV under 10% suggests low variability, while above 30% suggests high variability. Always inspect the histogram and box plot before drawing conclusions; statistics alone can be misleading without a look at the shape of the distribution.
Sample standard deviation divides the sum of squared deviations by (n−1) and is used when your data is a sample drawn from a larger population. Population standard deviation divides by n and is only correct when you have data for the entire population. Use the sample value (Bessel correction) by default — it is the unbiased estimator. Both are shown so you can pick the right one.
Variance is the average of squared deviations from the mean. Standard deviation is simply the square root of variance, which puts the result back into the same units as your original data. So if your data is in dollars, variance is in dollars-squared (hard to interpret), but standard deviation is in dollars (easy to interpret).
When two or more values share the highest frequency, the dataset is multimodal and all tied values are returned. If every value appears exactly once, there is no mode. The calculator labels datasets as unimodal, multimodal, or no mode automatically.
Quartiles use linear interpolation on the sorted data: Q1 is the 25th percentile, Q3 is the 75th percentile, and the median is the 50th. IQR (interquartile range) = Q3 − Q1 and represents the spread of the middle 50% of your data. The 1.5×IQR fences are used to flag potential outliers.
Use the geometric mean for averaging growth rates, ratios, or percentages compounded over time (it requires all positive values). Use the harmonic mean when averaging rates like speeds or P/E ratios — it gives less weight to large outliers. Both are shown as N/A if any value is zero or negative, since they are undefined in that case.
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