When might you use the mean and IQR (instead of the standard deviation)?

When might you use the mean and IQR (instead of the standard deviation)?

• A. Robust to outliers, for ranking data and real-world terms (positive or negative skew)
• B. Predicting the total value of the group when the data are normally distributed
• C. Data cleaning involves removing confounding variables
• D. The standard error is the standard deviation of sampling averages

Answer: (A)

Describing data when the distribution isn’t neat or contains extreme values calls for measures that aren’t pulled toward the extremes. The interquartile range does just that by capturing the spread of the middle 50% of scores, so it stays stable even with skew or a few outliers. You can still report a central tendency with the mean in practical contexts—for example, when data are used for ranking or when real-world values are interpreted as an average level—while using the mean with the IQR gives a concise picture of both the central value and the typical spread without overemphasizing outliers. In contrast, the standard deviation tends to be distorted by outliers and skew, making it less suitable in these situations. The other options relate to topics like predicting totals under normality, data cleaning, or sampling error, which aren’t about choosing how to summarize nonnormal data.

Describing data when the distribution isn’t neat or contains extreme values calls for measures that aren’t pulled toward the extremes. The interquartile range does just that by capturing the spread of the middle 50% of scores, so it stays stable even with skew or a few outliers. You can still report a central tendency with the mean in practical contexts—for example, when data are used for ranking or when real-world values are interpreted as an average level—while using the mean with the IQR gives a concise picture of both the central value and the typical spread without overemphasizing outliers. In contrast, the standard deviation tends to be distorted by outliers and skew, making it less suitable in these situations. The other options relate to topics like predicting totals under normality, data cleaning, or sampling error, which aren’t about choosing how to summarize nonnormal data.