In which of the following situations is the mean the most appropriate measure of center to report?

• A. Ratings on a 1–5 Likert scale (strongly disagree to strongly agree)
• B. Annual income in a city where a small number of residents earn extremely high incomes
• C. Test scores for a class that are approximately symmetric with no extreme outliers
• D. Home sale prices in a neighborhood with a few unusually expensive properties

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the nature of the data and the distribution in each situation. The mean is most appropriate when the data are approximately symmetric and do not have extreme outliers, because the mean is sensitive to extreme values.
2. Step 2: For ratings on a 1–5 Likert scale, recognize that this is ordinal data. Since the distances between scale points may not be equal, the median or mode is usually more appropriate than the mean.
3. Step 3: For annual income in a city with a few extremely high incomes, the distribution is likely right-skewed with outliers. The mean would be pulled upward by these extreme values, so the median is a better measure of center here.
4. Step 4: For test scores that are approximately symmetric with no extreme outliers, the mean is appropriate because the data distribution is balanced and the mean accurately reflects the central tendency.
5. Step 5: For home sale prices with a few unusually expensive properties, the distribution is skewed with outliers. The mean would be influenced by these high values, so the median is preferred over the mean.