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Computing Z-scores

 

Example: Compute the z-score for all teams in the American League in 2001, using the data below.  Compute the mean and standard deviation of the z-scores.  Conclude that the mean of z-scores is 0 and the standard deviation is 1.

 

Team

Home Runs

Team

Home Runs

1. Anaheim Angels

158

8. Minnesota Twins

164

2. Baltimore Orioles

136

9. New York Yankees

203

3. Boston Red Sox

198

10. Oakland Athletics

199

4.  Chicago White Sox

214

11.  Seattle Mariners

169

5.  Cleveland Indians

212

12.  Tampa Bay Devil Rays

121

 

6.  Detroit Tigers

139

13.  Texas Rangers

246

7.  Kansas City Royals

152

14.  Toronto Blue Jays

195

 

Press STAT and select 1: Edit. Clear L1 and L2. Enter the home run data from the table above into L1. Press STAT highlight CALC, select 1:1-Var Stats, and press 2nd  ENTER to obtain the population mean and standard deviation.

 

 

 

To obtain the Z-scores for the data set, Press STAT and select 1: Edit. Highlight L2 at the top of the second column and press ENTER. With the cursor flashing on the bottom line of the screen type in L1-179)/34.54.

 

 

The Z-score fore each data point in L1 will appear in L2. These Z-scores should have a mean of 0 and a standard deviation of 1. To check this, press STAT, highlight CALC, select 1:1-Var Stats, and press 2nd   ENTER.

 

 

Notice that the mean is 0. The population standard deviation is 1.00005509. This value is not exactly equal to 1 because we used a rounded value (34.54) for the standard deviation in our calculations.