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← Negative Z-Score - Intro to Descriptive Statistics

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Showing Revision 3 created 05/24/2016 by Udacity Robot.

  1. Since z equals the original value minus the mean, divided by standard deviation.
  2. In other words, the number of standard deviations that the original value is
  3. from the mean. Then a negative z score means that, the mean is greater than x.
  4. That must mean that x is somewhere down here. So that doesn't necessarily mean
  5. that the original value is negative, though it could be. It does mean that the
  6. original value is less than the mean. The original value is less than zero, it
  7. basically says the same thing as this first one, that the original value is
  8. negative. In this one, the original value x minus the mean is negative, must
  9. also be true. Because for the z score to be negative, then this is going to be
  10. negative, because the standard deviation is always positive. Just to review,
  11. remember when we calculated standard deviation, we squared all the deviations.
  12. So all the deviations are then positive, because if you square anything negative
  13. or positive, you get a positive number. And then we just took the average
  14. squared deviation, which is still positive, and then we took the square root,
  15. which is still positive. So remember that this standard deviation will always be
  16. positive. Which means that if the z score is negative, then this numerator must
  17. be negative. And that must mean that x is less than mu.