Which score indicates the highest relative position? a. A...

Which score indicates the highest relative position?
a. A score of 3.2 on a test with $\bar{X}=4.6$ and $s=1.5$
b. A score of 630 on a test with $\bar{X}=800$ and $s=200$
c. A score of 43 on a test with $\bar{X}=50$ and $s=5$

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Key Concepts

Standardization

This is the process of converting raw scores into a common scale, typically using the mean and standard deviation. Standardization allows for the comparison of scores that come from different distributions or scales.

Z-score

A z-score represents the number of standard deviations a raw score is from the mean. It is calculated by subtracting the mean from the raw score and dividing by the standard deviation, which helps in assessing the relative position of a score within its distribution.

Relative Position

This refers to the ranking or standing of a score in relation to all other scores in the distribution. By converting raw scores to z-scores, one can determine which score is most unusual or closer to the mean relative to others, thereby indicating its comparative performance.

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