Comparing z-scores: did Bobby do better than Cindy?

[roshan2004]

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??

 

[chiro]

Hey roshan2004.

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

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

Cindy
> (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?

 

[Stata]

The z-score reflects the distance an observed value is from the mean if the sample was distributed normally mean 0 var 1.