A data set is approximately symmetric and has no clear outliers. Which choice is most reasonable for describing the center and spread?
- Median and range, because mean cannot be used for symmetric data
- Mean and IQR, because range can never be used
- Mean and range, because there are no outliers to distort them (correct answer)
- Median and IQR, because they are always best
Explanation: This question tests relating measure choices to distribution shape, such as mean/median for center and range/IQR for spread based on symmetry and no outliers (mean standard for symmetric, range acceptable without distortion). For approximately symmetric data with no outliers, mean and median are both near center (equal in perfect symmetry), so mean is reasonable for center, and range is fine for spread as extremes aren't inflating it. Example: data like 10, 12, 14, 15, 16, 18, 20, mean (15) and range (10) work well; vs skewed 50, 52, 53, 54, 55, 80 needing median/IQR. The most reasonable choice is mean and range, because there are no outliers to distort them, fitting the symmetric shape. Common error: claiming median and IQR always best, or mean can't be used for symmetric (when it can), ignoring shape allows non-resistant measures. To relate: (1) identify shape (symmetric, no outliers), (2) consider resistance (not needed), (3) choose mean and range, (4) justify (mean average meaningful, range full spread accurate). Context: symmetric test scores use mean for class average, range for total variation.