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Calculate standard deviation, variance, mean, median, mode, range, and coefficient of variation. Get instant statistical analysis for your data set with step-by-step calculations.
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Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a dataset. It tells you how spread out the numbers are from their average value. A low standard deviation means data points are close to the mean, while a high standard deviation indicates data is spread over a wider range.
Sample Standard Deviation (s): Used when analyzing a subset of data from a larger population. Uses n-1 in the denominator (Bessel's correction) to provide an unbiased estimate.
Population Standard Deviation (Ļ): Used when you have data for the entire population. Uses n in the denominator. Less commonly used in practice.
For normally distributed data:
ā¢ 68% of data falls within 1 standard deviation
ā¢ 95% falls within 2 standard deviations
ā¢ 99.7% falls within 3 standard deviations
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Analyze experimental results, assess measurement precision, and determine statistical significance in studies.
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Our advanced standard deviation calculator provides comprehensive statistical analysis of your data. Simply enter your numbers separated by commas or spaces, and instantly get sample standard deviation, population standard deviation, variance, mean, median, mode, range, and coefficient of variation. Perfect for students, researchers, analysts, and professionals who need quick and accurate statistical calculations.
Standard deviation is essential when you need to understand data variability, compare consistency between datasets, identify outliers, assess risk in investments, perform quality control analysis, or conduct statistical hypothesis testing. It's widely used in finance for measuring volatility, in manufacturing for quality assurance, in research for analyzing experimental results, and in business for performance analysis.
Sample Standard Deviation:
s = ā[Ī£(xi - xĢ)Ā² / (n-1)]
Population Standard Deviation:
Ļ = ā[Ī£(xi - Ī¼)Ā² / n]
Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. A low standard deviation indicates that values tend to be close to the mean, while a high standard deviation indicates that values are spread out over a wider range.
Sample standard deviation (s) is calculated when you have a subset of data from a larger population, using n-1 in the denominator (Bessel's correction). Population standard deviation (Ļ) is used when you have data for the entire population, using n in the denominator. Sample standard deviation is more commonly used in statistical analysis.
To calculate standard deviation: 1) Find the mean (average) of the data, 2) Calculate the squared difference from the mean for each data point, 3) Find the average of these squared differences (variance), 4) Take the square root of the variance. For sample data, divide by (n-1); for population data, divide by n.
Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of variance. Variance is measured in squared units, while standard deviation is in the same units as the original data, making it more interpretable.
A high standard deviation indicates that data points are spread out over a large range of values, showing high variability or dispersion. This means the data is less consistent and more diverse. In contrast, a low standard deviation means data points are clustered closely around the mean.
For more information about standard deviation, statistics, and data analysis, visit these authoritative sources: