Math CentralQuandaries & Queries


Question from Imogen, a student:

I have an assignment that requires me to calculate the t scores, z scores, standard scores and percentile ranks of 3 children on a vocab task. I am struggling with how to calculate the correct T-scores for the children, my tutor has said that the sample has a mean of 50 and standard deviation of 10. So on a z- score of 2.0 (2 SD's from the mean) it would be 50 + 10+10 = T score of 70. However the Z- scores i have are not whole numbers so I am struggling with it, i have one that is 1.27 , another that is 0.47 and the last one is 0.80. If you could help me on how to calculate these to get T scores that would be great. Thanks.


Don't think of it as 50+10+10, think of it as 50 + (10 * 2.0)

Then find 50 + (10*1.27), etc.

Good Hunting!

PS: I notice that one of the three Z-scores you give is the sum of the other two. This may just be a coincidence. If however they are actually {-1.27,0.47,0.80}, their mean is exactly 0 [suggesting Z- scores based on a sample mean, which would be unusual for a small sample like this] but their standard deviation is not 1. Better check what you did.


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