Question

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

Explanation:

• Option A: Box plots show the median (a measure of average) and the spread. If the median (or center) of Olympic jumps' box plot is farther than that of U.S. qualifier jumps, we can say they are farther on average. This is a valid inference from box plots (comparing central tendency).
• Option B: Box plots have ranges (min to max). It's unlikely all Olympic jumps are farther than all U.S. qualifier jumps, as there could be overlap in the data (e.g., a long U.S. qualifier jump and a short Olympic jump). So this is false.
• Option C: To determine variation, we look at the interquartile range (IQR) or the overall range. If the Olympic jumps' box plot (including whiskers) is more spread out, we can say they vary more. But the question doesn't provide the actual box plots, but from typical box plot analysis, if we assume the context (maybe from a standard problem), but wait—actually, the key is: for A, average (median) can be compared. For B, "all" is too extreme (box plots have outliers or overlap in ranges). For C, "noticeably more"—but without the plot, but in the problem's context (assuming a common scenario where Olympic jumps have higher median (so A is true), B is false, and C—if the IQR or range of Olympic is larger, but maybe not. Wait, no—let's re-express:
• A: The median (or mean, but box plot uses median) of Olympic jumps is farther, so "on average" (median is a measure of central tendency) is correct.
• B: "All" Olympic jumps farther than "all" U.S. is impossible because box plots have minimum and maximum; there could be U.S. jumps that are farther than some Olympic jumps (overlap in data). So B is false.
• C: "Vary noticeably more"—the spread (IQR, range) of Olympic jumps. But without the plot, but in the problem's options, A is correct. Wait, maybe the original problem's box plots (not shown here) have Olympic jumps with higher median (so A is true), B is false (since there's overlap), and C—maybe not. But based on box plot interpretation:
• A is correct because we can compare central tendency (median) from box plots.
• B is incorrect (all vs all is too extreme, as box plots have ranges that can overlap).
• C: If the Olympic jumps' box (IQR) and whiskers are more spread, then C is correct, but if not, then not. But in typical problems, if Olympic jumps are at a higher level, their median is higher (A is correct), and maybe their variation is more or less. But the key is: A is a valid inference (average via median), B is not (all vs all), C—depends on spread. But in the options, A is correct. Wait, maybe the answer is A (and maybe C, but let's think again).

Wait, the question is about what can be gathered from box plots. Box plots show:

• Median (line in box) – central tendency (average-like).
• IQR (box length) – variation.
• Range (whiskers) – total variation.

So:

• A: If Olympic's median is farther, then average (median) is farther. Correct.
• B: "All" Olympic jumps farther than "all" U.S. – box plots have minimum and maximum. So there could be U.S. jumps with higher values than some Olympic jumps (overlap). So B is false.
• C: "Vary noticeably more" – if Olympic's IQR or range is larger, then yes. But without the plot, but in the problem's context (maybe from a standard problem where Olympic jumps have higher median (A correct), and maybe C is not, or is. But the key is: A is correct.

Answer:

A. The Olympic jumps were farther on average than the U.S. qualifier jumps.