How to use this statistics calculator
Enter a list of numbers separated by commas, spaces or line breaks. Choose Sample when the values are observations drawn from a larger group; choose Population when they are the full group you want to describe. The calculator reports the count, mean, median, mode, range, variance and standard deviation. Its distribution view shows where the entered values sit between the minimum and maximum. Keep the units consistent: for example, combine test scores with test scores, rather than mixing scores and ages.
What the numbers mean
The mean is the sum of all values divided by their count. The median is the middle value after sorting, or the average of the two middle values when the count is even. A mode is a value that occurs most often; several values can tie. If every value appears once, this tool reports no mode. The range is maximum minus minimum.
Variance measures squared distances from the mean. For a population, add those squared distances and divide by the number of values, n. For a sample, divide by n − 1. Standard deviation is the square root of variance, so it is expressed in the original unit. Sample standard deviation is normally larger for the same data because its divisor is smaller. Neither measure tells you whether the data are normally distributed or whether an outlier is an error.
Checked example
Enter 2, 4, 4, 4, 5, 5, 7, 9. The eight values sum to 40, so the mean is 5. The middle values are 4 and 5, giving a median of 4.5. Four occurs most often, so the mode is 4; the range is 9 − 2 = 7. The squared distances from the mean sum to 32. Population variance is 32 ÷ 8 = 4 and population standard deviation is 2. Sample variance is 32 ÷ 7, about 4.5714, and sample standard deviation is about 2.1381.
Input limits and interpretation
You can enter at most 5,000 finite numbers, including signed decimals and scientific notation. A sample needs at least two values because dividing by n − 1 would otherwise divide by zero; a one-value population has zero variance and standard deviation. Extremely large values that cannot be calculated reliably are rejected. If your question is about a course outcome rather than a dataset, use the final exam grade calculator.
Frequently asked questions
Should I choose sample or population?
Use population when your list includes every member of the group you are describing. Use sample when the list stands in for a larger group. The choice changes variance and standard deviation, but not the mean or median.
Why can there be more than one mode?
Two or more values may share the highest repeat count. The calculator lists each tied value. If no value repeats, it displays no mode.
Does standard deviation show the direction of a change?
No. It measures spread around the mean, not whether values are increasing over time. Preserve the order and context of observations when you need a trend.
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