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Find mean, median, mode, range, and population or sample standard deviation from your data.
Practice statistics →Enter 1 to 1000 numbers separated by commas, spaces, or new lines. Press Calculate to see the mean, median, mode, range, population and sample standard deviations, count, and sorted list; include repeated values rather than removing them.
Mean is the sum divided by the number of values. Median is the middle of the sorted list, or the average of the two middle values for an even count. Mode identifies the most frequent repeated value or tied values; range is largest minus smallest. Population standard deviation is σ = √(Σ(x − μ)²/n); sample standard deviation is s = √(Σ(x − x̄)²/(n − 1)). The calculator shows each distinct value’s deviation from the mean and its squared contribution. Sample standard deviation is undefined for one value; identical values have standard deviation zero. These summaries describe a dataset, not the probability of a future event.
Enter 2, 4, 4, 6, 9. Sum = 25, so mean = 5; median = 4; mode = 4; range = 7. Squared deviations from 5 are 9, 1, 1, 1, and 16, which sum to 28. Population standard deviation = √(28/5) ≈ 2.366; sample standard deviation = √(28/4) ≈ 2.646.
For 7, 7, 7, the mean is 7 and every deviation is zero, so both population and sample standard deviations are 0. For one value, 7, population standard deviation is 0; sample standard deviation is undefined because n − 1 = 0.
It depends on the data. The mean uses every value and is sensitive to unusually large or small observations; the median focuses on the middle and is less affected by extremes.
Yes. If two or more repeated values tie for the highest frequency, all are shown. If every value occurs once, this tool reports no mode.
Yes, as long as each value is finite. Separate numbers clearly, and do not use thousands separators inside a value: enter 1000, not 1,000.
Population standard deviation divides the sum of squared deviations by n; sample standard deviation divides by n − 1 to estimate spread from a sample. Both are shown. Sample standard deviation is undefined for one value; if all values are identical, both results are zero. Use the Box Plot Calculator for quartiles and interquartile range.
Use a box plot to visualize spread and quartiles, or the Probability Calculator for outcome counts rather than data summaries. The statistics lesson explains when each measure is useful. Related tools: Box Plot Calculator, Probability Calculator. Read the Statistics lesson or practice statistics to build confidence without relying on a calculator.