Math Problem Statement
Solution
Let's analyze the box-and-whisker plots for the two cities (City A and City B) to answer each question:
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(a) Which city had the highest noon temperature?
- The highest noon temperature is represented by the upper "whisker" (the furthest point to the right). City B has the highest temperature reaching around 95°F, while City A's highest temperature is slightly below this value.
- Answer: City B
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(b) Which city had noon temperatures with a larger interquartile range (IQR)?
- The interquartile range (IQR) is the length of the box in each plot, which represents the range between the first quartile (Q1) and the third quartile (Q3). City B has a visibly larger box than City A, indicating a larger IQR.
- Answer: City B
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(c) Which city had a smaller range of noon temperatures?
- The range is the distance between the smallest and largest values (represented by the ends of the whiskers). City A has a smaller range because its whiskers are closer together compared to City B.
- Answer: City A
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(d) Which city had a larger median noon temperature?
- The median is indicated by the line inside each box. City A's median line is further to the right (around 75°F) compared to City B's median (around 70°F).
- Answer: City A
Would you like further explanations or details on any of these answers?
Here are five additional questions to deepen your understanding of box-and-whisker plots:
- What does it mean if a city has a larger interquartile range (IQR)?
- How does the position of the median within the box reflect the skewness of data?
- Why might a city have a larger range of temperatures compared to another?
- How can box-and-whisker plots help in comparing datasets in terms of variability?
- What information can be inferred about outliers from these plots?
Tip: Box-and-whisker plots are a powerful tool for visualizing the spread and central tendency of data, especially useful in comparing different datasets directly.
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Math Problem Analysis
Mathematical Concepts
Box-and-Whisker Plot
Interquartile Range
Range
Median
Formulas
Interquartile Range (IQR) = Q3 - Q1
Range = Maximum - Minimum
Theorems
Descriptive Statistics
Suitable Grade Level
Grades 6-8
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