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Converting standard scores

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Why it is possible to easily convert standard scores from one scale to another. When using these score listed below the mean and standard deviation of each of the transformed scores and the theoretical rationale for their equivalency for an example.

Person A z-score of 1.0

CEEB Score = 600
IQ Score = 115
AP Score = 82%
T-Score = 60

Person B z-score of 0.00

CEEB Score = 500
IQ Score = 100
AP Score = 50%
T-Score = 50

Person C z-score of -1.00

CEEB Score = 400
IQ Score = 85
AP Score = 15%
T-Score = 40

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This solution helps go through converting standard scores.

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The reason we can convert between scales easily is because we can use the mean and standard deviation of a scale to relate it to a z score. For each of the participants above, we are given a z score. The z score codes how many standard deviation units the person's score is from the mean. So a z score of ...

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