Variability insight

Standard Deviation & Sigma Playground

Drop any set of observations to instantly compute sample (s) and population (σ) standard deviation, variance, mean, range, and run-length insight. The live curve redraws with your sigma so you can explain spread visually.

Handles up to 5,000 numbers Ignores blanks & stray text Exports chart via right-click

Author · Pawan

Reviewer · Kushal Singh

1. Paste or type dataset

Accepts commas, tabs, spaces, or new lines.

Tip: Copy a spreadsheet column, paste, then hit “Calculate”.

Sample SD (s)

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Population SD (σ)

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Mean (μ)

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Count (n)

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Sample variance

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Population variance

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2. Visual curve

Color bands mark ±σ zones

Purple tails capture ~0.1% of data, gold spans the central 68%. Drag or pinch to explore the density.

3. Interpretation cues

Enter at least two numbers to unlock insight.

Methodology checklist

Sample vs population: Sample uses n−1 in the denominator to keep estimators unbiased; population divides by n.
Precision: Results keep four decimal places unless values are integers.
Data cleansing: Any token that cannot become a finite number is skipped (NaNs, blanks, stray text).
Chart: We draw a normal distribution using your sample mean and σ. Actual distributions may differ, but the bell curve is ideal for presenting spread.

FAQ

Do I need to sort or centre the data?

No. We compute the mean directly and subtract μ from every value under the hood, so unsorted data is fine.

What about text like NA or blank cells?

Use “Remove invalids” to strip them from the textarea automatically. The calculator also ignores them during computation.

Can I export the curve?

Right-click or long-press on the chart and choose “Save image as…” to download the latest bell curve.

References

Author

Pawan leads the data tooling stack at CalcArena. His focus is on trustworthy formulas, reproducible visuals, and communication tips statisticians can lift straight into reports.

Reviewed by · Kushal Singh, AI Research Program Manager