9: Measurements

9.1

Measurements Vary

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• Key Idea 1: Whenever we measure, measurement variability and hence measurement error must creep in...
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    Discussion

    15 measurements were made of the height of a stack of textbooks (each measurement was made by a team of 2 people). Here are the results, in centimeters:  24.1 24.7 23.6 23.8 22.3 22.8 23.6 23.5 24.0 24.0 24.4 23.6 23.8 23.8 24.3

• Key Idea 2: The random errors resulting from successive measurements of an unknown quantity can be viewed as a random sample from the large (conceptually infinite) population of all possible measurement errors...

• Key Idea 3: According to the normal law of error, most measurement data are normally distributed...
  
  

  Discussion

  Therefore, about 2/3 of the time our measurements would fall within 1 standard deviation of the true value, and about 95% of the time within 2 standard deviations of the true value.

  
  
  
• Key Idea 4: Values in a data set that are exceptionally far away from the mean are called outliers...
  
  

  Discussion

  One widely-used rule is that a data point is called an outlier if its distance from the sample mean is more than 3 times the sample standard deviation. Outliers merit attention - they may reflect a problem with that specific observation.  Measurement outliers can be the result of some sort of procedural error, such as misplacing a decimal point or grossly misusing a piece of equipment. It is common statistical practice in measurement to remove them.

• Key Idea 5: It is standard practice to improve accuracy by averaging multiple measurements...
  

Exercises

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