METHODS OF DATA ANALYSIS
MEASURES OF DISPERSION
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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She didn’t take the test yet.
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She scored 1.5 standard deviations below the average.
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She did better than most people.
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No clue
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Detailed explanation-1: -Joanne’s Z-score is-1.5. What does this mean? She did better than most people. She scored 1.5 standard deviations below the average.
Detailed explanation-2: -A z-score of 1.5, then, means that a value is 1.5 standard deviations greater than the mean. Z-scores can be negative if they are below the mean, so for the three-sigma rule, 68% of the values fall between the z-scores of-1 and 1.
Detailed explanation-3: -For z-scores, it always holds (by definition) that a score of 1.5 means “1.5 standard deviations higher than average”. However, if a variable also follows a standard normal distribution, then we also know that 1.5 roughly corresponds to the 95th percentile.
Detailed explanation-4: -A score of 1 indicates that the data are one standard deviation from the mean, while a Z-score of-1 places the data one standard deviation below the mean.