Which statement is false concerning measures of statistical dispersion?
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Answer: C. The standard deviation is equal to the square of the sum of the squares of all the differences (deviations) between each score and the mean, divided by the number of scores
Explanation
Standard deviation requires taking the square root of the variance rather than simple division. Dividing squared deviations directly by the number of scores calculates variance instead of standard deviation. Calculating standard deviation accurately always involves the final step of square root extraction. Statistical dispersion measures how spread out a set of numerical data values is. Variance is the average of the squared differences from the mathematical mean value. Standard deviation is expressed in the same original units as the collected data.
Researchers use standard deviation to understand data variability in scientific experiments. Financial analysts rely on dispersion metrics to evaluate investment portfolio risk levels. Standardized testing scores utilize standard deviation to compare individual student performances. The range accurately represents the simple mathematical difference between maximum and minimum values. Standard deviation remains the most widely reported measure of variability in research. Variance is mathematically defined as the square of the standard deviation value.
- Subject
- Psychology
- Category
- Psychology
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- —
- Difficulty
- medium
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