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Z score

  1. Oct 1, 2012 #1
    Bobby and Cindy are in different math classes. Bobby got a 75 on his test and Cindy got a 70 (surprisingly low for children of an architect). Bobby’s class had a mean of 80 and a standard deviation of 5. Cindy’s class had a mean of 75 and a standard deviation of 10. Who did better on their test, Bobby or Cindy?
    I calculated the z score of both and found Bobby's z score higher than Cindy's. Does it means that he has done better than Cindy's??
  2. jcsd
  3. Oct 2, 2012 #2


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    Science Advisor

    Hey roshan2004.

    In R I calculated the Z-score for both giving:

    > (75-80)/5
    [1] -1

    > (70-75)/10
    [1] -0.5

    This shows that Cindy's Z-score is greater than Bobby's which is opposite to your statement.

    Can you show us how you calculated the Z-scores for both people?
  4. Oct 2, 2012 #3
    The z-score reflects the distance an observed value is from the mean if the sample was distributed normally mean 0 var 1.
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