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Questions and Answers
What is the extent to which the scores vary around their central tendency called?
What is the extent to which the scores vary around their central tendency called?
What is the main limitation of using the range to measure variability?
What is the main limitation of using the range to measure variability?
What is the average distance between the scores and the mean called?
What is the average distance between the scores and the mean called?
Why is the standard deviation a more common measure of variability than the range?
Why is the standard deviation a more common measure of variability than the range?
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What can be said about the two distributions in Figure 12.4?
What can be said about the two distributions in Figure 12.4?
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What is the range of the self-esteem scores in Table 12.1?
What is the range of the self-esteem scores in Table 12.1?
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Why might the range be a misleading measure of variability in certain cases?
Why might the range be a misleading measure of variability in certain cases?
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What is the standard deviation of the top distribution in Figure 12.4?
What is the standard deviation of the top distribution in Figure 12.4?
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What is the primary purpose of finding the difference between each score and the mean in calculating standard deviation?
What is the primary purpose of finding the difference between each score and the mean in calculating standard deviation?
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What is the term for the mean of the squared differences in calculating standard deviation?
What is the term for the mean of the squared differences in calculating standard deviation?
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What is always true about the squared differences in calculating standard deviation?
What is always true about the squared differences in calculating standard deviation?
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What is the final step in calculating standard deviation?
What is the final step in calculating standard deviation?
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What is the role of variance in statistical analysis?
What is the role of variance in statistical analysis?
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What is the symbol used to represent the variance?
What is the symbol used to represent the variance?
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Study Notes
Measures of Variability
- Variability of a distribution is the extent to which scores vary around their central tendency.
- Distributions with the same central tendency can have different variabilities.
Range
- The range is a simple measure of variability, calculated as the difference between the highest and lowest scores.
- Example: Range of self-esteem scores in Table 12.1 is 24 - 15 = 9.
- The range can be misleading when there are outliers.
Standard Deviation
- The standard deviation is the average distance between scores and the mean.
- Example: Standard deviations of the distributions in Figure 12.4 are 1.69 for the top distribution and 4.30 for the bottom one.
- Computing the standard deviation involves:
- Finding the difference between each score and the mean.
- Squaring each difference.
- Finding the mean of these squared differences (variance).
- Finding the square root of the variance.
Variance
- The variance is the mean of the squared differences between scores and the mean (symbolized as SD²).
- The variance is always positive.
- Although the variance is a measure of variability, it generally plays a larger role in inferential statistics than in descriptive statistics.
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Description
This quiz explores the concept of variability in data distributions, including measures of central tendency and spread.
