How to calculate standard deviation

Definition: Standard deviation is a statistical measure of the amount of variation or dispersion of a set of values.

A standard deviation table can be useful for identifying outliers, understanding the distribution of the data, and making inferences about a population based on a sample.

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To calculate the standard deviation of a set of data, you can use the following formula:

Sample Standard Deviation:

s = sqrt(∑(x_i - x̄)^2 / (n - 1))

where x_i represents each data point, x̄ represents the mean of the data, n represents the number of data points, and ∑ represents the sum of all the differences.

Population Standard Deviation:

σ = sqrt(∑(x_i - μ)^2 / N)

where μ represents the mean of the population, N represents the number of data points in the population, and the other variables are defined as in the sample standard deviation formula.

In both cases, you first need to find the mean of the data, then subtract each data point from the mean, square the result, sum all the squared differences, and divide by either n - 1 for the sample standard deviation or N for the population standard deviation. Finally, take the square root of the result to get the standard deviation.

Standard Deviation	Standard Deviation Calculator
Sample Standard Deviation	Sample Standard Deviation Calculator
Population Standard Deviation	Population Standard Deviation Calculator
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