The symmetric bell-shaped probability distribution in which about 68.3 % of values fall within ±1 standard deviation, 95.45 % within ±2 and 99.73 % within ±3. It is assigned to an imported certificate uncertainty, to the mean of repeated readings and, through the central limit theorem, to the combined result when several comparable contributions are summed. To convert a normal expanded uncertainty to a standard uncertainty, divide by its stated coverage factor.
Reference cert gives 0.02 percent at k equals 2, treat it as a normal distribution and divide by two.
Also heard as
- Gaussian distribution
- Gaussian
- bell curve
Related terms
Probability density function, the curve describing how likely each possible value of a quantity is.
Standard deviation
The usual measure of scatter in a set of values, the square root of the average squared deviation from the mean.
Coverage factor
The multiplier applied to combined standard uncertainty to obtain expanded uncertainty, usually k = 2.
Student t-distribution
A bell-shaped distribution with heavier tails than the normal, used to set coverage factors when data are limited.
Two sigma
Shop shorthand for an uncertainty quoted at k = 2, roughly 95 percent coverage.