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There are three sigma symbols, an upper case, a lower case and an end of the sentence case. The capital letter case is used as summation. The lower case is used to represent variance in statistics. The lower case is also used to represent stress in mechanics and physics. The end of sentence case is generally not used. Reference link: http://en.wikipedia.org/wiki/Sigma.
Six-sigma is a quality control program that strives for less than 3.4 defects in a million opportunities; or near perfection. In statistics, sigma represents areas under a bell curve (similar to IQ normal curves). If all defects fall outside the shaded area (outside three sigma on either side, where the center is perfect and all shaded areas are acceptable) there is very little shaded area (defects) left.
formula for finding mean through direct mean method: sigma fi xi /sigma fi
sigma represents standard deviation. In a normal distribution, +/- 1 sigma from the mean, for instance, corresponds to approximately 67% of the area under the normal distribution. +/- 2 sigma corrresponds to 95% of the area and +/- 3 sigma from the mean corresponds to 99% of the area under a normal distribution. The area that is covered under +/- six sigma from the mean corresponds to nearly 100% -- that is, the part of the area NOT under that +/- 6 sigma is in the 10^-15 range or 1/1,000,000,000,000,000. The six sigma name borrows from this to suggest that the method gives this degree of certainty: that in 999,999,999,999,999 in 1,000,000,000,000,000 cases the result will be predictable. It does nothing, however, to explain how an agricultural process management methodology applies to other fields.
the mean is important in statistics because you will find out your average and can compare that mean to other things..