Math Problem Statement
Before sending track and field athletes to the Olympics, the U.S. holds a qualifying meet. The upper dot plot shows the distances (in meters) of the top [8] shot putters in the preliminary round of the [2012] Olympic games. The lower dot plot shows the top [8] throwers in the shot put at the U.S. qualifying meet. A dot plot is divided into 2 parts labeled, U.S. Qualifier and Olympic Preliminary. The horizontal axis is labeled, Distance, in meters, from 19 to 21.5, in increments of 0.1 meter. The portion of the dot plot dedicated to U. S. Qualifier has dots above the following points; 19.15, 19.17, 19.5, 19.7, 19.8, 19.95, 20.25, and 21.22. The portion of the dot plot dedicated to Olympic Preliminary has dots above the following points; 20.43, 20.5, 20.55, 20.75, 20.8, 21.05, 21.15, and 21.45. All values estimated. [19] [19.5] [20] [20.5] [21] [21.5] Which pieces of information can be gathered from these dot plots? Choose all answers that apply: Choose all answers that apply: (Choice A) The top [8] Olympic shot putters in the preliminary round threw farther on average than the top [8] U.S qualifiers. A The top [8] Olympic shot putters in the preliminary round threw farther on average than the top [8] U.S qualifiers. (Choice B) The distances of the top [8] Olympic shot putters vary noticeably more than those of the top [8] U.S. qualifiers. B The distances of the top [8] Olympic shot putters vary noticeably more than those of the top [8] U.S. qualifiers. (Choice C) None of the above C None of the above
Solution
Let's analyze the dot plots and the given information carefully.
Dot Plot Information:
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U.S. Qualifier (Top 8 throwers):
- Distances: 19.15, 19.17, 19.5, 19.7, 19.8, 19.95, 20.25, 21.22 meters.
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Olympic Preliminary (Top 8 throwers):
- Distances: 20.43, 20.5, 20.55, 20.75, 20.8, 21.05, 21.15, 21.45 meters.
Step-by-Step Analysis:
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Average Distance Comparison (Choice A):
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The U.S. Qualifier distances range from 19.15 meters to 21.22 meters.
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The Olympic Preliminary distances range from 20.43 meters to 21.45 meters.
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Conclusion for Average: The average distance for the Olympic Preliminary group seems higher, as all the throwers in this group have distances above 20 meters, whereas the U.S. Qualifiers have values below 20 as well as some closer to 21. Therefore, it appears that the top Olympic shot putters threw farther on average than the U.S. qualifiers.
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Choice A is true.
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Variation in Distances (Choice B):
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U.S. Qualifier range: 19.15 to 21.22 meters.
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Olympic Preliminary range: 20.43 to 21.45 meters.
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When we compare the spread of the distances:
- The U.S. Qualifiers' distances range from 19.15 meters to 21.22 meters, a spread of 2.07 meters.
- The Olympic Preliminary distances range from 20.43 meters to 21.45 meters, a spread of 1.02 meters.
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Conclusion for Variation: The distances for the Olympic group appear more tightly packed, with a smaller range compared to the U.S. Qualifiers.
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Choice B is false, as the Olympic group has less variability, not more.
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Final Answer:
- Choice A: True (The top 8 Olympic shot putters threw farther on average than the top 8 U.S. qualifiers).
- Choice B: False (The distances of the top 8 Olympic shot putters vary less, not more, than those of the U.S. qualifiers).
- Choice C: False (At least one of the choices is true, so this is incorrect).
To Summarize:
The correct answer is Choice A.
Would you like further clarification on how to calculate the average or variation of distances, or do you have any other related questions?
Here are some follow-up questions to explore the concept further:
- How do you calculate the average distance of a set of values?
- How do you calculate the range of a set of data points?
- What does it mean for data to have "more variability" versus "less variability"?
- What is the significance of "outliers" in determining the variation of a dataset?
- How could you visualize the spread of data more clearly using a different type of plot (e.g., box plot)?
Tip: When comparing two datasets, always consider both the average (central tendency) and the spread (variability) to get a more complete picture.
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Math Problem Analysis
Mathematical Concepts
Data Representation
Statistics
Dot Plots
Mean
Range
Variation
Formulas
Range = Max Value - Min Value
Mean = (Sum of all values) / (Number of values)
Theorems
Comparison of averages and ranges in data sets
Suitable Grade Level
Grades 6-8
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