Z-scores

What is a z-score?

A z-score measures the distance, or how many standard deviations, a data point is from the mean. A z-score of 2 means your data point is 2 standard deviations above the mean. A z-score of 0 means your data point is the mean, and a z-score of -2 means your data point is 2 scores below the mean.


What is the formula?

  •  z= (x-µ)/𝜎
  • Where z is the z- score
  • X is your data point
  • µ is the mean
  • 𝜎 is the standard deviation

What are z-scores used for?

  • z-scores can be used to compare two different data values on two different scales
  • z-scores can also be used to find what percent of the the data lies above and below your data values
  • z-scores are also used in some hypothesis tests

Example:

You took the sat and your best friend took the act. You scored a 780 on the sat and your friend scored a 12 on the act. The average for the sat scores this year was a 1500 with a standard deviation of 250. And the average for the act scores this year was 20.8 with a standard deviation of 4.8.

Screen Shot 2017-06-28 at 5.35.55 PMScreen Shot 2017-06-28 at 5.43.08 PM

-2.88<-1.83

Therefore, your friend did better than you did.

 

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