QQuestionStatistics
QuestionStatistics
A z-score of 2.5 would indicate what with respect to the raw score's proximity to the distribution mean?
A. That the raw score lies precisely 2.5 standard deviations above the mean
B. That the modal category for the distribution lies 2.5 standard deviations below the mean
C. That the raw score lies 2.5 standard deviations below the mean
D. That the distribution has a mean of 2.5
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understanding Z-Scores
- $$\sigma$$ is the standard deviation
A z-score represents the number of standard deviations a raw score is from the mean of a distribution. The formula for a z-score is: Where:
Step 3:: Interpreting a Z-Score of 2.5
A z-score of 2.5 means the raw score is 2.5 standard deviations above the mean of the distribution.
Step 4:: Analyzing the Options
- Option A: Exactly correct. A z-score of 2.5 indicates the raw score is 2.5 standard deviations above the mean. - Option B: Incorrect. This refers to the modal category, which is not related to the z-score. - Option C: Incorrect. This would be a z-score of - 2.5, not 2.5. - Option D: Incorrect. The z-score does not define the mean of the distribution.
Final Answer
The z-score of 2.5 indicates that the raw score lies precisely 2.5 standard deviations above the mean.
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