Difference between revisions of "Sigma"

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(1 SIGMA)
(2 SIGMA)
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If someone says that an error is 1 sigma, then that person is referring to the greatest possible error in between the lines marked with - 1 sigma to + 1 sigma in the bell curve (see the curve above).  Add the percentages of the two regions under the bell to get about 68%.  There is a 68% chance that the error will not exceed the value stated.
 
If someone says that an error is 1 sigma, then that person is referring to the greatest possible error in between the lines marked with - 1 sigma to + 1 sigma in the bell curve (see the curve above).  Add the percentages of the two regions under the bell to get about 68%.  There is a 68% chance that the error will not exceed the value stated.
  
=== 2 SIGMA ===
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=== 2 SIGMA - 95% Chance ===
  
If someone says that an error is 2 sigma, then that person is referring to the greatest possible error in between the lines marked with - 2 sigma to + 2 sigma in the bell curve (see the curve above).  Add the percentages of the two regions under the bell to get about 95%.  There is a 95% chance that the error will not exceed the value stated.
+
If someone says that an error is 2 sigma, then that person is referring to the greatest possible error in between the lines marked with -2 sigma to +2 sigma in the bell curve (see the curve above).  Add the percentages of the four regions under the bell between the - and + sigma lines to get about 95%.  There is a 95% chance that the error will not exceed the value stated.
 +
 
 +
=== 3 SIGMA - 95% Chance ===
 +
 
 +
If someone says that an error is 3 sigma, then that person is referring to the greatest possible error in between the lines marked with -3 sigma to +3 sigma in the bell curve (see the curve above).  Add the percentages of the six regions under the bell to get about 95%.  There is a 95% chance that the error will not exceed the value stated.
  
  

Revision as of 23:57, 3 October 2011

Most have heard of the "bell curve" in mathematics. This is the shape that describes the probability that a given percentage of measurements will fall within a certain region under a standard bell curve. This shape is found in nature - so its one that mathematicians use often.

This shape of the standard bell curve is called "Normal Distribution" or "Gausian Distribution."

Bellcurve.jpg


Contents

HOW SIGMA PERTAINS to the BELL CURVE

A statistical measurement called "standard deviation" is also referred to as "sigma" on the horizontal axis of a bell curve. Basically, this is a measurement of how much the measurements vary from the center value by a distance of a value called "sigma" on either side of the center of the curve.

1 SIGMA

If someone says that an error is 1 sigma, then that person is referring to the greatest possible error in between the lines marked with - 1 sigma to + 1 sigma in the bell curve (see the curve above). Add the percentages of the two regions under the bell to get about 68%. There is a 68% chance that the error will not exceed the value stated.

2 SIGMA - 95% Chance

If someone says that an error is 2 sigma, then that person is referring to the greatest possible error in between the lines marked with -2 sigma to +2 sigma in the bell curve (see the curve above). Add the percentages of the four regions under the bell between the - and + sigma lines to get about 95%. There is a 95% chance that the error will not exceed the value stated.

3 SIGMA - 95% Chance

If someone says that an error is 3 sigma, then that person is referring to the greatest possible error in between the lines marked with -3 sigma to +3 sigma in the bell curve (see the curve above). Add the percentages of the six regions under the bell to get about 95%. There is a 95% chance that the error will not exceed the value stated.


Now three sigma is 3* the standard deviation, which statistically mean that 99.73% of the time a measurement is made it will be within 3*the standard deviation of the actual value. It is thus a way to compare how good the measurement method is.

In similar ways 2 sigma means within 95% of the actual value and 6 sigma means as close to always as is resonable to ever need.