Question

What does it mean to write: π av ± σ , or π av ± 2σ , or π av ± 3σ . How much % of normal data distribution is included in each ?

Answer 1

It is a measure of the confidence you have in the mean value of the data points.

68% of the data is within 1 standard deviation of the mean.
95% is within 2 standard distributions
97.7% is within 3 standard distributions.

Explanation:

This assumes a normal distribution.

In the graphic the mean is `mu` and the standard deviation is designated by `sigma`.

A commonly used statistical test is the 95% confidence limit which is `+-2sigma`.

The criteria in particle physics can be much stricter. The existence of The Higg's Boson was verified at a confidence of `5sigma`.

This means that the odds are 1 in 3.5 million that the results from CERN were due to chance.