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.
Standard Deviation Calculator
The standard deviation can be calculated using the following steps:
- Calculate the mean of the data set.
- Subtract the mean from each data point and square the result.
- Sum the squared differences.
- Divide the sum by either (n - 1) for sample standard deviation or (N) for population standard deviation.
- Take the square root of the result.
Standard deviation calculator using mean
Sample Standard Deviation:
s = sqrt(∑(x_i - x̄)^2 / (n - 1))
Population Standard Deviation:
σ = sqrt(∑(x_i - μ)^2 / N)
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.
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| Sample Standard Deviation | Sample Standard Deviation Calculator |
| Population Standard Deviation | Population Standard Deviation Calculator |
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