If you learn that your score on an exam was 81 and the mean was 69, would you be more satisfied if the standard deviation was 6 or if it was 15?
Question
If you learn that your score on an exam was 81 and the mean was 69, would you be more satisfied if the standard deviation was 6 or if it was 15?
Solution
To answer this question, we need to understand what standard deviation means. Standard deviation is a measure of how spread out numbers are. A low standard deviation means that most of the numbers are close to the average (mean), while a high standard deviation means that the numbers are more spread out.
If your score is 81 and the mean is 69:
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If the standard deviation is 6, it means that most of the scores are within 6 points of the mean (69). So, your score of 81 is significantly higher than most of the scores, which are close to 69.
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If the standard deviation is 15, it means that the scores are spread out over a wider range. Your score of 81 is not as significantly higher than the mean (69) as in the first case.
So, you would be more satisfied if the standard deviation was 6 because it means your score is significantly higher than most of the other scores.
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