What is standard deviation?
Answer
Standard deviation is a measure of dispersion that shows how much the data values spread out from their mean.
The working
Meaning
It quantifies the average distance of data values from the mean. A small standard deviation means data is clustered near the mean; a large one means it is spread out.
Symbol and relation
It is denoted by σ (sigma) and equals the positive square root of the variance. So σ = √(variance).
Formula
For n values with mean x̄, σ = √[ Σ(xᵢ − x̄)² ÷ n ]. Each deviation from the mean is squared, averaged, then square-rooted.
Why square root
Variance is in squared units, so taking the square root brings the measure back to the original units of the data.
Example
For data 2, 4, 6 the mean is 4, deviations are −2, 0, 2, so σ = √[(4 + 0 + 4) ÷ 3] = √(8÷3) ≈ 1.63.
Stuck on something else?
Type your own doubt into the solver and get the full working in seconds — free, for physics, chemistry, maths and biology.
Open the solverRelated doubts