z-Scores |
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z-Scores are standardized values that can be used to compare scores in different distributions. |

Take this example: For the past two years, Joe has been in a bowling league.

First Year Stats:

League Average = 181

Standard Deviation = 12

Joe’s Score in Final Game = 187

Second Year Stats:

League Average = 182

Standard Deviation = 5

Joe’s Score in Final Game = 185

Compared to the rest of the league, in which year was Joe’s score in the final game better?

Figure 1. |
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We can calculate a z-score for each year:

Figure 2. |
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We can then plot the z-scores and compare their placement on the distribution. From the graphs below you can see that compared to the rest of the league, Joe had a better score in his second year.

Figure 3. |
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