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← SD of Standardized Distribution - Intro to Descriptive Statistics

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Showing Revision 3 created 05/25/2016 by Udacity Robot.

  1. Now remember, when we calculate the z score of any value in the distribution,
  2. we first subtract the mean which shifts the distribution without changing the
  3. shape so that zero is now the mean. And when we divide by the standard
  4. deviation, we then change the shape. Let's look at it this way. We have any
  5. distribution, with mean, mu, and standard deviation, sigma. Which basically
  6. means that sigma is one standard deviation away from the mean. After we
  7. standardize this distribution, what is going to be the z-score of sigma? Well,
  8. remember when we subtract mu, we shift it so that mu is now zero. So now, the
  9. z-score of sigma is going to be sigma minus zero divided by sigma, which is
  10. sigma divided by sigma, which is 1. So, the z-score of any value, that's one
  11. standard deviation away from the mean, will then be 1 after we standardize it.
  12. Which means that the new standard deviation of this normalized distribution, or
  13. standard distribution, is 1.