Math Problem Statement

The noon temperatures (in Fahrenheit) for two cities were recorded over a given month. The box-and-whisker plots summarize the noon temperatures for each city. Use the box-and-whisker plots to answer the following questions: (a) Which city had the highest noon temperature? (b) Which city had noon temperatures with a larger interquartile range (IQR)? (c) Which city had a smaller range of noon temperatures? (d) Which city had a larger median noon temperature?

Solution

Let's analyze the box-and-whisker plots for the two cities (City A and City B) to answer each question:

  1. (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
  2. (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
  3. (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
  4. (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:

  1. What does it mean if a city has a larger interquartile range (IQR)?
  2. How does the position of the median within the box reflect the skewness of data?
  3. Why might a city have a larger range of temperatures compared to another?
  4. How can box-and-whisker plots help in comparing datasets in terms of variability?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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