If the distribution of test scores is skewed, which statistics are preferred to summarize central tendency and spread?

If the distribution of test scores is skewed, which statistics are preferred to summarize central tendency and spread?

• A. Mean and standard deviation
• B. Median and interquartile range
• C. Mode and range
• D. Mean and range

Answer: (B)

When data are skewed, use a measure that isn’t pulled by extreme values. The median serves as a robust center because it reflects the middle point of the data regardless of how far the tails extend. The interquartile range focuses on the spread of the central 50% of scores, ignoring the extremes and giving a stable sense of variability. Mean and standard deviation, in contrast, are sensitive to outliers and the long tail of a skewed distribution, which can distort both the typical score and the perceived spread. The range depends entirely on the extreme values and can be heavily influenced by a single outlier, making it less reliable. The mode isn’t consistently informative for central tendency in many datasets, and it doesn’t capture spread well.

When data are skewed, use a measure that isn’t pulled by extreme values. The median serves as a robust center because it reflects the middle point of the data regardless of how far the tails extend. The interquartile range focuses on the spread of the central 50% of scores, ignoring the extremes and giving a stable sense of variability.

Mean and standard deviation, in contrast, are sensitive to outliers and the long tail of a skewed distribution, which can distort both the typical score and the perceived spread. The range depends entirely on the extreme values and can be heavily influenced by a single outlier, making it less reliable. The mode isn’t consistently informative for central tendency in many datasets, and it doesn’t capture spread well.