Standard Deviation Calculator

Standard deviation is one of the most fundamental measures in statistics — it quantifies how spread out a set of numbers is relative to their average. A low standard deviation means values cluster tightly near the mean, indicating consistency; a high standard deviation means values are spread widely, indicating high variability. This calculator computes the population standard deviation, variance, mean, and count for exactly six values. It is ideal for quick classroom problems, quality control checks, sports score analysis, or any situation where you have a small fixed dataset and need a fast statistical summary without setting up a spreadsheet. Population standard deviation divides the sum of squared differences by n, making it appropriate when your six values represent the complete dataset rather than a sample drawn from a larger group. The variance output is the square of the standard deviation and is useful in further statistical calculations, while the mean gives you the central reference point. Together, these four outputs provide a complete descriptive summary of your dataset.

The calculator starts by computing the arithmetic mean of all six values by summing them and dividing by six. It then finds each value's deviation from the mean (value − mean), squares each deviation to make all values positive and to penalise larger deviations more heavily, and sums those squared deviations. Dividing that sum by the count of values (n) gives the population variance — the average squared distance from the mean. Finally, the square root of the variance is taken to bring the measure back to the same units as the original data, producing the population standard deviation. This calculator uses the population formula (÷ n) rather than the sample formula (÷ n−1), which is appropriate when the six values represent the complete dataset rather than a sample drawn from a larger group.