Standard Deviation Calculator
Interactive Statistics Tool
Standard Deviation Calculator
Analyze variability, compare sample and population SD, and explore how each observation affects the spread of your data.
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Population SD
1.60
Sample SD
1.69
Mean
5.00
Variance
2.56
N
8
Population standard deviation
σ
=
√
1
N
Σi=1N
(xi − μ)2
The current dataset has a mean of
μ = 5.00
and a population standard deviation of
σ = 1.60
.
Drag any observation to explore variability
Data Distribution
Frequency of observations across the dataset
Observations
Drag points above or edit the dataset
Population Standard Deviation
σ = √[ Σ(x − μ)² / N ]
Population standard deviation describes the amount of variation when the dataset represents the entire population.
Sample Standard Deviation
s = √[ Σ(x − x̄)² / (n − 1) ]
Sample standard deviation uses n − 1 degrees of freedom and is commonly used when estimating population variability from a sample.