Question

which pieces of information can be gathered from these box plots? choose all answers that apply: a the distances in the olympic final were farther on average. b the distances in the olympic final were all greater than the u.s. qualifier distances. c the distances in the olympic final varied noticeably more than the u.s qualifier distances. d none of the above

Explanation:

• Option A: Box plots show the median (a measure of central tendency, similar to average in interpretation for comparison) and spread. If the median (or central tendency) of Olympic final distances is higher, we can say they are farther on average. This is a valid inference from box plots (comparing central tendencies).
• Option B: "All" distances in Olympic final being greater than U.S. qualifier is incorrect. Box plots have ranges (minimum to maximum), so there can be overlap in the data points (e.g., the minimum of Olympic final could be less than the maximum of U.S. qualifier, or vice versa, but "all" is too extreme—box plots don’t guarantee all values in one group are above another).
• Option C: Variation in box plots is shown by the interquartile range (IQR) and the overall range. If the IQR or range of Olympic final distances is larger, we can say they varied more. However, without seeing the actual box plots, but from typical reasoning: if the question is structured to have A as correct (since "all" in B is wrong, and C’s "noticeably more" is not necessarily implied without plot, but A is about average/central tendency which box plots can show). Wait, correction: Let's re - evaluate. Box plots: the line inside the box is the median (a measure of central tendency). So if the median of Olympic final is higher, we can say "farther on average" (since median represents the middle value, so central tendency is higher). For C: variation is about spread (IQR, range). But the key is: A is correct because median (a measure of average - like central tendency) can be compared. B is wrong (all values? No, box plots have min and max, so overlap is possible). C: "noticeably more"—without the plot, but in general, if the box (IQR) or whiskers (range) of Olympic final are wider, but the question is about what can be gathered. Wait, the standard analysis:

1. For A: Box plots display the median (a measure of central tendency). If the median of Olympic final distances is greater than that of U.S. qualifier, we can conclude the distances in Olympic final were farther on average (since median is a representative value of the dataset’s center). So A is a valid inference.

1. For B: Saying "all" distances in Olympic final were greater than U.S. qualifier is wrong. Because box plots have a minimum value for Olympic final and a maximum value for U.S. qualifier—there could be values in Olympic final that are less than some values in U.S. qualifier (e.g., Olympic final’s min < U.S. qualifier’s max). So B is incorrect.

1. For C: "Varied noticeably more"—variation is measured by IQR (interquartile range) or range. Without seeing the box plots, we can’t be sure if the variation is "noticeably more". But A is a more straightforward inference from box plots (comparing central tendency via median). So A is correct.

Answer:

A. The distances in the Olympic final were farther on average.