Math Problem Statement

Two geometry classes with the same number of students took a final exam. The box-and-whisker plots summarize the test scores for each class. Use the box-and-whisker plots to answer the following questions: (a) Which class had a higher median test score? (b) Which class had test scores with a larger interquartile range (IQR)? (c) Which class had the highest test score? (d) A score above 70 is considered passing. Which class had more passing scores?

Solution

Let's analyze the box-and-whisker plots step by step to answer the questions.

  1. Median test score (Question a):
    The median is represented by the line inside each box:

    • Class A: The median is at approximately 75.
    • Class B: The median is lower, approximately 70.
      Answer: Class A had a higher median test score.
  2. Interquartile Range (IQR) (Question b):
    The IQR is the length of the box (distance between Q1 and Q3):

    • Class A: The box is smaller, indicating a smaller IQR.
    • Class B: The box is larger, indicating a larger IQR.
      Answer: Class B had a larger interquartile range (IQR).
  3. Highest test score (Question c):
    The highest test score is indicated by the right whisker:

    • Class A: The highest score is 95.
    • Class B: The highest score is approximately 92.
      Answer: Class A had the highest test score.
  4. Passing scores (above 70) (Question d):
    Scores above 70 are passing:

    • Class A: The entire box (middle 50%) and the right whisker are above 70. Most scores are passing.
    • Class B: The left whisker and part of the box are below 70. Fewer scores are passing.
      Answer: Class A had more passing scores.

Final Answers:

(a) Class A
(b) Class B
(c) Class A
(d) Class A


Would you like a deeper explanation of any part? Let me know!

Related Questions:

  1. How do you calculate the interquartile range (IQR) for a boxplot?
  2. What are the five-number summary components in a boxplot?
  3. Why is the median a better measure of center for skewed data than the mean?
  4. How can you identify outliers using a boxplot?
  5. How would the boxplot change if a single very low test score were removed?

Tip: In a box-and-whisker plot, the length of the box gives the IQR, and whiskers show the range of the data excluding outliers.

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Math Problem Analysis

Mathematical Concepts

Box-and-Whisker Plots
Interquartile Range (IQR)
Median
Data Distribution

Formulas

Interquartile Range (IQR) = Q3 - Q1

Theorems

Five-Number Summary in Statistics

Suitable Grade Level

Grades 6-8