Arithmetic Mean Calculator
FreeCalculate the arithmetic mean, median, mode, range, and both population and sample standard deviation of a dataset, with a dot plot and histogram.
Runs entirely in your browser.
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What this tool does
This tool calculates the arithmetic mean of a list of numbers, right in your browser, along with the median, mode, range, minimum, maximum, and both population and sample standard deviation and variance, plus a dot plot and histogram visualization.
How It Works
The arithmetic mean is Mean = (sum of all values) / (count of values). The median is the middle value after sorting (or the average of the two middle values when the count is even). The mode is the most frequently occurring value or values, if every value is unique there is no mode. Range is maximum minus minimum. Population variance is the average of each value's squared distance from the mean, Variance = Σ(x − mean)² / n, while sample variance divides by (n − 1) instead of n, Variance = Σ(x − mean)² / (n − 1), to correct for the bias of estimating spread from a subset. Standard deviation is simply the square root of the corresponding variance.
Problems it solves
- Getting a full statistical summary of a dataset, mean, median, mode, spread, without switching between separate tools.
- Seeing at a glance whether outliers might be skewing the mean, by comparing it against the median.
- Choosing the right variance formula (population vs. sample) for coursework or reporting.
- Visualizing how a dataset is distributed with a dot plot and histogram.
Frequently asked questions
›What is the difference between the arithmetic mean and the median?
The mean is the sum of all values divided by how many there are, so a single very large or very small value can pull it up or down. The median is the middle value once everything is sorted, so it is much less affected by extreme outliers.
›Why does this tool show both a population and a sample standard deviation?
It depends on whether your numbers are the entire group you care about (population) or just a sample drawn from a larger group. Population standard deviation divides by the count, sample standard deviation divides by count minus one, which corrects for the fact that a sample tends to slightly underestimate the true spread.
›Why is the sample standard deviation "N/A" for a single number?
The sample formula divides by (count − 1), so with only one value that becomes division by zero, there is no way to estimate spread from a single data point.
›What does it mean when there is "no mode"?
Mode is the value that appears most often. If every value in your list is different, none of them repeats more than any other, so there is no meaningful "most common" value.
›Can I paste data from a spreadsheet?
Yes, the input accepts numbers separated by commas, spaces, or line breaks, so pasting a single column or row copied from a spreadsheet works without any reformatting.
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