Z Score

Who is the best athlete?

• Tiger Woods
• Tom Brady
• Venus Williams
• We can't really tell because they all play different sports.

Statistics gives us a way to compare events that are measured differently.  Which of the following is an example of events that are measured differently?

• Jess' test score vs. Mia's test score
• Payton Manning's pass completion vs. Aaron Rodgers pass completion
• Quin's ACT score vs. Jake's SAT score
• My Fitbit steps (lol) vs. Ms. Kladis' Fitbit steps

In order to compare, we can "standardize" the scores.  This means we are going to convert the scores to a "third party" measure called a Z-score.  
What does standardize mean?

• Convert to a z-score
• Make me take a test
• something about the common core
• no clue

Hopefully you answered
"z-score".
 A z-score tells us how many standard deviations a score is from the mean.
What is another word for "mean"?

• nasty
• average
• median
• good looking

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By the way, what is standard deviation?

• good question
• how standardly something deviates
• average distance that data points are from the average
• Idk but I should probably find out pretty soon

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Standard deviation tells us how spread out a symmetric distribution is. 
Since a Z-score tells us how many standard deviations away from average something is, what does a high Z-score mean?

• It's way higher than average
• tl:dr
• you're in trouble?
• you need a doctor

Adam's Z-score on a test is +2.5.  What does this mean?

• He'd better start studying.
• He did better than EVERYONE.
• He scored 2.5 standard deviations above the average.
• He did terrible.

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Joanne's Z-score is -1.5.  What does this mean?

• She didn't take the test yet.
• She scored 1.5 standard deviations below the average.
• She did better than most people.
• No clue

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Z-scores are calculated by subtracting the mean from the score and then dividing by the standard deviation.  Which of the following is a formula that describes this calculation?

• Z = (score - mean) / stand. devation
• Z = (mean - score) / stand. dev.
• Z = score/stand. dev/ mean
• Z = dragonball

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If Gonzalo's score is 87, the class average is 82, and the SD is 4, what is Gonzalo's Z-score?

• -1.25
• +1.25
• +1.20
• +1.02

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