How and when did we get two forms of sigma?

1. Why does sigma have two forms?
2. Why are there 3 sigmas?
3. Why does sigma have a final form?

Why does sigma have two forms?

Really the three different letters are there for these reasons: One is a captial (Σ) One is a lowercase letter (σ) One is a lowercase letter as well but it's only used on the last letter of a word or sentence.

Why are there 3 sigmas?

Three-sigma limits are used to set the upper and lower control limits in statistical quality control charts. On a bell curve, data that lie above the average and beyond the three-sigma line represent less than 1% of all data points.

Why does sigma have a final form?

For uppercase they used the classical inscription letters, and for lowercase they tried to imitate cursive handwriting. This gave us the three modern forms of sigma, Σ/σ/ς. There was no real reason to distinguish σ from ς any more, but at that point it was what readers were used to.