Mean, median and standard deviation calculator

How the calculation works

These measures summarize a set of numbers. The three most used:

Mean: add everything and divide by the count — the data's "center of gravity".
Median: sort the values and take the middle one (average of the two middle if even). It is not distorted by extremes.
Standard deviation: how much the data spread around the mean.

Sample standard deviation:

s = √( Σ(x − mean)² ÷ (n − 1) )

With outliers, the median better represents the "typical" value. That's why incomes and house prices are usually reported by the median.

Low = data clustered near the mean (consistent). High = spread out. Two classes can share a mean grade but differ wildly in spread.

Grades 7, 8, 9: mean 8, median 8, deviation 1.
With an outlier (7, 8, 9, 50): the mean jumps to 18.5, but the median stays at 8.5.

Sample or population standard deviation?

We use the sample one (divides by n−1), the most common in applied statistics.

Standard deviation vs variance?

Variance is the average of squared deviations; standard deviation is its square root, preferred because it shares the data's unit.

When to use median over mean?

When extreme values distort the mean — income, house prices, response times. The median better represents the "typical" value.