Empirical Rule (68-95-99.7)

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Calculate Normal Distribution coverage bands (68-95-99.7 rule).

Parameters

Mean (μ)

Std Dev (σ)

Coverage Bands

1-Sigma Band (68.27%)85.00 — 115.00±1σ Range

2-Sigma Band (95.45%)70.00 — 130.00±2σ Range

3-Sigma Band (99.73%)55.00 — 145.00±3σ Range

About this calculator

Overview

The Empirical Rule, also known as the 68-95-99.7 rule, states that for a Normal Distribution, almost all data falls within three standard deviations of the mean. This rule is a quick way to estimate the spread of data and identify potential outliers in a bell-shaped dataset.

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Pro Tips

Use this for datasets that follow a bell curve shape.
The 1-sigma band covers roughly 68% of the data.
The 3-sigma band covers 99.7% of the data, meaning it captures nearly everything.

Fun Facts

"In manufacturing, "Six Sigma" targets 99.99966% defect-free products. This means the process is so precise that a product only fails if it falls more than 6 standard deviations away from the mean!"
"The rule applies strictly to normal distributions; however, Chebyshev's Inequality provides a more general (but less precise) version for any distribution."
"Approximately 1 in 370 observations will fall outside the 3-sigma range by chance in a perfect normal distribution."

Formula: Range = μ ± (k * σ)