Paste your data to calculate sample or population standard deviation — with variance, coefficient of variation, z-scores, σ-zone breakdown, and a histogram with normal curve overlay.
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Use the calculator above to paste your data and instantly calculate sample or population standard deviation, with variance, coefficient of variation, z-scores, a sigma-zone breakdown and a histogram with normal-curve overlay. Standard deviation is the foundation measurement of variation — and variation is the enemy in any Lean Six Sigma programme.
Standard deviation measures the typical distance of data points from the mean. A low value means the process is tight and consistent; a high value means the process is variable. It is the single most useful statistic in process improvement and the basis of nearly every other inferential method.
Population σ = √(Σ(xᵢ−μ)² ÷ N). Sample s = √(Σ(xᵢ−x̄)² ÷ (n−1)). Variance is the square of standard deviation. The (n−1) divisor for samples produces an unbiased estimator and matters most for small samples — get this wrong and capability indices, p-values and CIs are all subtly off.
Two lines both have a mean weight of 100g. Line A: σ = 0.4g. Line B: σ = 1.2g. Same average — but Line B varies three times as much. Customers will see Line B defects (overfill, underfill) far more often, even though "average" is identical.
Standard deviation feeds straight into Cp / Cpk, control charts and Sigma Level. Halving σ on Line B would deliver dramatic improvements in defect rate without any change to the mean — which is why variation reduction is the heart of Six Sigma.
Standard deviation is the lever Six Sigma is named after. Reducing σ produces lower defect rates, tighter capability and more predictable performance — without any change to average performance.
Use standard deviation whenever you want to characterise the spread of any continuous data set — process outputs, cycle times, weights, dimensions, financial returns.
σ is the unit of measurement for Six Sigma itself. 6σ between the process mean and the nearest spec limit equals 3.4 DPMO. Almost every quantitative tool in Six Sigma uses σ as a building block.
Once you have σ, calculate capability indices and chart the data on a control chart. If σ is large, run a DMAIC project to identify the dominant source of variation and reduce it.
Combine standard deviation with control charts, capability indices and DOE to convert the headline σ into specific variation-reduction actions.
A measure of the typical distance of data points from the mean. Low σ means tight, consistent data; high σ means spread, variable data.
Population σ uses N in the denominator and assumes you have the entire population. Sample s uses (n−1) and corrects for the bias that arises from using a sample to estimate the population value.
Six Sigma takes its name from σ. A process with 6σ between the mean and the nearest spec limit produces 3.4 DPMO — world-class quality.
It depends on context — σ is judged against the specification width. A useful rule: process σ should be roughly 1/6 of the spec width or less for capable processes.
σ ÷ mean, expressed as a percentage. It allows fair comparison of variation between processes with very different means (e.g. weights of 1g items vs 1kg items).
Want to understand how standard deviation fits into process variation and improvement? The Yellow Belt covers this in full.
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