Statistics Calculator (Mean, Median, Mode & SD)

About the Statistics Calculator

Descriptive statistics summarize a dataset using measures of central tendency (such as the Mean / Average and Median) and measures of dispersion (such as Variance and Standard Deviation).

Enter any comma-separated list of numbers above to compute the count, sum, mean, variance, and standard deviation instantly.

Mean, Variance & Standard Deviation Formulas

For a dataset of N values x₁, x₂, ..., x_N:

How to Calculate Mean and Standard Deviation

1. Find the Mean: Add all numbers in the dataset together and divide by the total count N.
2. Compute Squared Deviations: Subtract the mean from each data point and square each result.
3. Average and Take the Square Root: Divide the sum of squared deviations by N to get the variance, then take the square root to get the standard deviation.

Worked Example: For the dataset 10, 20, 30, the mean is (10+20+30)/3 = 20. Squared deviations are (−10)² + 0² + 10² = 200, giving variance 200/3 ≈ 66.67 and SD ≈ 8.165.

Frequently Asked Questions (FAQ)

What does a low vs. high standard deviation mean?

A low standard deviation indicates that the data points are clustered closely around the mean, whereas a high standard deviation indicates that the values are spread out over a wider range.