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How do you calculate the standard deviation of a sample?

To calculate the standard deviation of a sample, please follow the steps below:

Collect a sample of data points.

Calculate the average (arithmetic mean) of the sample by dividing the sum of all data points by the number of data points.

Calculate the deviation of each data point from the mean by subtracting the value of each data point from the mean.

Square each deviation to eliminate negative values ​​and reinforce the significance of the deviations.

Calculate the mean of the squared deviations by dividing the sum of all squared deviations by the number of data points in the sample. This value is called the variance.

Calculate the standard deviation by taking the square root of the variance.

Here is the formula to calculate the standard deviation of a sample:

Standard deviation = √(Σ(x - x̄)² / (n - 1))

x is a data point in the sample

x̄ is the mean of the sample

n is the number of data points in the sample

It is important to note that the formula uses the divisor (n - 1) instead of just n. This is because the sample estimate needs a correction for the bearish in variance that occurs when considering the Sample mean used to estimate the population mean. This is known as the "Bessel Correction".

By following these steps and applying the formula, you can calculate the standard deviation of your sample.