Question 621:

Asked on February 8, 2009

Tags: Z-Score

1

Answer:

No answer provided yet.

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.