Standard Deviation Calculator

1. Enter your data set. Type or paste numbers separated by commas, spaces, or semicolons. Example: 85, 90, 78, 92, 88. You need at least 2 values. The calculator handles up to hundreds of data points.
2. Choose sample or population. Use "Sample" (divides by n-1) when your data represents a subset of a larger group, like surveying 100 customers to estimate all customers. Use "Population" (divides by N) when you have data for every single member of the group.
3. Read the statistics. Results include mean, median, mode, range, variance, standard deviation, and interquartile range (IQR). The sorted data view helps spot outliers.

Example: test scores 70, 75, 80, 85, 90 have mean = 80, sample SD = 7.91. About 68% of scores would be expected between 72.09 and 87.91 in a similar test.

Mean (μ):         μ = Σxᵢ / n

Population SD (σ): σ = √(Σ(xᵢ - μ)² / N)
Sample SD (s):     s = √(Σ(xᵢ - x̄)² / (n-1))

Variance:         σ² or s² (SD squared)

Steps to calculate by hand:
1. Find the mean
2. Subtract mean from each value, square each difference
3. Sum all squared differences
4. Divide by N (population) or n-1 (sample)
5. Take the square root

Worked example: data = 2, 4, 4, 4, 5, 5, 7, 9