What is the formula for calculating standard deviation for a sample?

The formula for calculating the standard deviation of a sample is s = √[Σ(xi - x̄)² / (n - 1)]. This formula is designed to estimate the variability or spread of a set of sample data points around the sample mean (x̄).

In this formula, "xi" represents each individual data point, "x̄" is the sample mean, and "n" is the number of observations in the sample. The numerator Σ(xi - x̄)² sums the squared differences between each data point and the mean, capturing how much each data point deviates from the mean. Using (n - 1) in the denominator, rather than n, corrects for bias and provides an unbiased estimate of the population standard deviation when the calculation is based on a sample rather than the entire population. This correction is known as Bessel's correction and is important, especially in smaller samples, to ensure that the estimate doesn't underestimate the population standard deviation.

The other formulas provided either do not properly account for this correction or describe different statistical calculations. This makes the chosen formula the most appropriate for calculating the standard deviation from sample data.