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Question 621:



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To convert each raw value to a z-score we need to first find the mean and standard deviation for this sample. The mean is the sum of the values divided by the total or 75/5 = 15.  The standard deviation is the average distance to the mean for each value and can be found using the standard deviation calculator or the excel function =STDEV(). See also the Standard deviation tutorial. We get the result of 4.   Now we can convert each raw score to a z-score or standardized score by subtracting it from the mean and dividing that result by the standard deviation.


  1. (10-15) /4 = -1.25
  2. (20-15) /4 = 1.25
  3. (12-15) /4 = -0.75
  4. (17-15) /4 = 0.5
  5. (16-15) /4 = 0.25


So each value is now in standardized form relative to the sample mean and standard deviation. We see the more extreme values, which are further from the mean of 15 have a higher z-score.

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