Z - Scores
Oh, Dear - Now we know we our French Taking Room is Sad!
Z = (60 - 70) / 10
Z = -1.0
Her Z - score in negative and below the mean.
Nuances About the Z-Score:
1. The Z -
score can be positive
or negative.
Positive is above the mean.
Negative is below the mean.
2. The Mean
of the Z
scores is Zero.
If you got the class average on a test - your Z -score = 0.
Because Z would be (Mean-Mean)/0 = 0.
3. The Standard Deviation of the Z distribution = 1. We will discuss this later.
A Really Big Concept!
Z -Scores can be Turned into Percentages
Here's the deal - if you know a Z-score - you know what percent or proportion of scores are above and below that score.
It's like slicing
a pie. 
Cut it in quarters and you know that each quarter as 25% of the pie.
Let's slice the Normal Curve
The distribution holds 100% of the scores or a proportion of 1.0
The gray line cuts it in half. So - half are below and half above.
If you received the average score on the test (Z = 0.0), you did better than 50% of the class.
What about cutting the distribution in another place?
l Calculus types have calculated the percents above and below any Z-Score.
l We mentioned this is Workshop #1.
l You statistics book has a table with this information in it.
Some Examples:
Our Physics Students:
1. The score of 60 was 1 Standard Deviation (Z= 1.0) above the mean.
The table would tell me that there are 84.13% of scores below.
2. The score of 84 was 3.4 SDs above the mean (Z = 3.4).
The table tells me that there were 99.97% scores below it.
No wonder these kids are happy.
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