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Basics of Coordinate Metrology
Unit 12: Evaluation of the Measurement - Standard distribution

Step 4 of 6
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This normal distribution of scattering can be described by two parameters: 

  • x  average of measured values

  • s  standard deviation


 
The smaller the value s, the smaller the scattering.

        

The parameter s can additionally be used to give information on the confidence in the feature values: Thus, in the standard distribution, a total of 95% of all feature values are in the range between -2s (seen from the average value) and +2s (see on the right).
   

Example:

In 18 measurements of a cylindrical bore under repetition conditions, the following values were obtained (in mm): 
 1,769   1,712   1,709   1,775   1,739    1,778   1,712   1,763   1,795  
1,767   1,782   1,765   1,741   1,735    1,703   1,758   1,782   1,752  

From these values it can be concluded that the average valueof the measurements is 1,752 mm and the standard deviation is 0.027 mm. Accordingly, the confidence range in which 95% of all measured values are located is the range from 1,752-(2·0,027) mm to 1,752+(2·0,027) mm, that is, 1,698 mm to 1,806 mm.