Standard Deviation Calculator | Statistical Analysis Tool
Calculate standard deviation, variance, mean, and other statistical measures with our free online calculator. Perfect for data analysis and statistics.
Category: Math
Standard Deviation Calculator
Calculate standard deviation, variance, mean, and other statistical measures with our free online calculator.
Category: Math
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Example Standard Deviation Calculation
Learn how to use this calculator with this example
Frequently Asked Questions
What is standard deviation?
Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates the values are spread out over a wider range.
How is standard deviation calculated?
Standard deviation is calculated by: 1) Finding the mean of the data set, 2) Subtracting the mean from each value and squaring the result, 3) Finding the mean of the squared differences, 4) Taking the square root of that mean.
What's the difference between population and sample standard deviation?
Population standard deviation is used when data from an entire population is available. Sample standard deviation is used when you only have data from a subset of the population. The sample standard deviation formula uses n-1 in the denominator (Bessel's correction) to provide an unbiased estimate.
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Frequently Asked Questions
What is standard deviation?
Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
How do you calculate standard deviation?
To calculate standard deviation: 1) Find the mean of the data set; 2) Subtract the mean from each value and square the result; 3) Calculate the mean of these squared differences; 4) Take the square root of that mean. The formula is: σ = √[(Σ(x - μ)²)/N], where σ is standard deviation, Σ means 'sum of', x represents each value, μ is the mean, and N is the number of values.
What's the difference between sample and population standard deviation?
Population standard deviation is used when you have data for the entire population. Sample standard deviation is used when you only have data from a sample of the population. The main difference in calculation is that sample standard deviation uses n-1 in the denominator (Bessel's correction) instead of N to provide an unbiased estimate.
What are common applications of standard deviation?
Standard deviation is used in finance for risk assessment, in quality control to measure consistency, in scientific research to analyze experimental results, in weather forecasting to understand variability, in medicine for establishing normal ranges, and in education to normalize test scores.