Math Problem Statement

The noon temperatures (in Fahrenheit) for two cities were recorded over a given month. Using the box-and-whisker plots for City A and City B, determine: (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 larger median noon temperature? (d) Which city had a smaller range of noon temperatures?

Solution

Based on the provided box-and-whisker plots, here are the answers to the questions:

(a) Which city had the highest noon temperature?

  • City B had the highest noon temperature, as shown by its upper whisker reaching the farthest to the right.

(b) Which city had noon temperatures with a larger interquartile range (IQR)?

  • City A had a larger interquartile range (IQR). The box for City A is wider, indicating a larger spread between the first and third quartiles.

(c) Which city had a larger median noon temperature?

  • City B had a larger median noon temperature, as its median line is positioned further to the right compared to City A.

(d) Which city had a smaller range of noon temperatures?

  • City B had a smaller range of noon temperatures. Its whiskers span a narrower interval than those of City A.

Would you like any further clarification on these points?

Here are 5 related questions for further exploration:

  1. What is the specific numerical range for each city's noon temperatures?
  2. How would the mean temperature compare between these two cities?
  3. What does a larger interquartile range tell us about temperature variability?
  4. Why might one city have a more consistent temperature range than the other?
  5. How do outliers, if any, affect the interpretation of box-and-whisker plots?

Tip: When interpreting box-and-whisker plots, the length of the box shows the interquartile range, while the whiskers indicate the overall spread of the data.

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Math Problem Analysis

Mathematical Concepts

Statistics
Data Interpretation
Box-and-Whisker Plot Analysis
Interquartile Range (IQR)
Range and Median

Formulas

Interquartile Range (IQR) = Q3 - Q1
Range = Maximum Value - Minimum Value

Theorems

Five-number summary in box-and-whisker plots

Suitable Grade Level

Grades 6-8