Calculate the mean, variance, and standard deviation for any data set. Choose between population or sample formulas for accurate statistical analysis.
Count (n):
0
Sum:
Arithmetic Mean (x̄):
Variance (s² or σ²):
Standard Deviation (s or σ):
A lower standard deviation indicates that the data points tend to be close to the mean, while a higher standard deviation indicates that the data points are spread out over a wider range.
Standard deviation quantifies the variation in a dataset by calculating the square root of the average squared deviations from the mean.
Formula: σ = sqrt(Σ(x - μ)2 / N)
σ = sqrt(Σ(x - μ)2 / N)
Example: For a Sample dataset of 10, 12, and 14.
Use 'Sample' when your data is a subset of a larger group. It uses n-1 (Bessel's correction) to provide an unbiased estimate of the population variance.
Variance measures the average squared distance from the mean in squared units, while Standard Deviation is the square root of variance, returning the result to the original units.
Squaring ensures all differences are positive so they don't cancel each other out, and it gives more weight to outliers far from the mean.
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