Standard Deviation Calculator
Calculate the standard deviation of a set of numbers.
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Calculate the Standard Deviation of a Data Set
Our Standard Deviation Calculator computes the standard deviation, variance, and mean of a set of numbers, and differentiates between sample and population data.
What is Standard Deviation?
Standard deviation is a fundamental concept in statistics that measures the spread or dispersion of a dataset relative to its mean (average). A low standard deviation indicates that the data points are clustered closely around the mean, suggesting consistency. A high standard deviation indicates that the data points are spread out over a wider range of values, indicating more variability. It is a crucial tool for understanding the volatility of investments, the consistency of experimental results, and the distribution of data in many fields.
How It Works: The Formula
The calculator first finds the mean (μ) of the data set. Then, it calculates the variance (σ²) and finally the standard deviation (σ).
Variance (σ²): Σ(xᵢ - μ)² / N
Standard Deviation (σ): √σ²
Here, 'xᵢ' represents each value in the data set, 'μ' is the mean, and 'N' is the total number of values. For a *sample* standard deviation, the variance formula divides by N-1 instead of N.
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 (the average), 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, you first find the mean of your data set. Then, for each number, you subtract the mean and square the result. You find the average of these squared differences (this is the variance). Finally, you take the square root of the variance. Our calculator automates this multi-step process.
What is the difference between sample and population standard deviation?
You use population standard deviation when your data represents the entire population of interest. You use sample standard deviation when your data is a smaller sample of a larger population. The key difference in the formula is that for sample variance, you divide by (n-1) instead of n, where n is the number of data points. This provides a better estimate of the population's true standard deviation.
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