Calculate a full set of descriptive statistics, including mean, median, mode, standard deviation and quartiles, from a list of numbers.
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This is a comprehensive descriptive statistics tool covering measures of central tendency (mean, median, mode), spread (range, variance, standard deviation, interquartile range), and both population and sample versions of variance and standard deviation, alongside basic figures like sum, count, minimum and maximum.
Population statistics treat your data as the complete data set, dividing by the total count. Sample statistics treat your data as a sample drawn from a larger population, dividing by count minus one, which slightly increases the result to account for the extra uncertainty of estimating from a sample.
Quartiles split the sorted data into four equal parts: Q1 is the value below which 25% of the data falls, and Q3 is the value below which 75% falls. The interquartile range (IQR = Q3 − Q1) captures the spread of the middle 50% of the data and is less sensitive to outliers than the full range.
For the data set 4, 8, 15, 16, 23, 42 (6 numbers, sum 108): mean = 108 ÷ 6 = 18. Sorted, the values are already in order, so the median (average of the two middle values, 15 and 16) is 15.5. Every value is unique, so there's no mode. Range = 42 − 4 = 38. Population variance = 151.6667 and population standard deviation ≈ 12.3153; sample variance (dividing by count−1 = 5 instead of 6) = 182 and sample standard deviation ≈ 13.4907. Q1 ≈ 9.75, Q3 ≈ 21.25, and the interquartile range (Q3 − Q1) is 11.5.
Reading the population standard deviation when you meant to use the sample figure (or vice versa), the two rows are both shown, but they answer different questions and can differ noticeably on small data sets.
Expecting the IQR to be affected by extreme outliers the way the full range is, IQR only looks at the middle 50% of the data, so a single very high or low value barely moves it, that's precisely why it's often preferred for skewed data.
Assuming Q1 and Q3 always land exactly on a value in your data set, depending on the quartile method and how the count divides, quartiles can fall between two data points, this calculator interpolates in that case.
Use population statistics if your data represents the entire group you care about. Use sample statistics if your data is a subset used to estimate characteristics of a larger population, this is the more common case in research and surveys.
This calculator combines everything from both of those tools into one comprehensive result, and adds quartiles, IQR, sum, min and max, useful when you want a full statistical summary of a data set in a single place.
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