2: Centers and Spread

2.7

Standard Deviation

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• Key Idea 1: The standard deviation, sometimes abbreviated SD, is the square root of the variance...
  
  

  Discussion

  The Greek letter s2 is also used to denote the variance. Taking the square root of the variance puts this measure on the same scale as the data (e.g. "inches" instead of "inches squared")

  
  
  
• Key Idea 2: The standard deviation will often be close to the mean absolute deviation...
  
  
  

  Discussion

  The mean absolute deviation is more robust against a small proportion of unusually large or small numbers. The standard deviation has important statistical properties and is mathematically convenient.

  
  
  
• Key Idea 3: When we take a sample of data and use its standard deviation to estimate the standard deviation of a larger population, dividing by n-1 instead of n gives a better estimate...
  
  
  

  Discussion

  See Section 11.8 for more detail. For now, if you are using a computer or calculator, be aware of which method is used.

Exercises

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