Math Problem Statement

Use the box-and-whisker plots to answer questions about Class A and Class B test scores.

Solution

Let's analyze the box-and-whisker plots for Class A and Class B:

Observations:

  1. Range:
    The range is the difference between the minimum and maximum values (whiskers).

    • Class A: Range ≈ 55 to 90 → Range = 90 - 55 = 35.
    • Class B: Range ≈ 60 to 80 → Range = 80 - 60 = 20.
      Class B has a smaller range of test scores.
  2. Highest Test Score:
    The highest test score corresponds to the maximum value (rightmost whisker).

    • Class A: Maximum ≈ 90.
    • Class B: Maximum ≈ 80.
      Class A has the highest test score.
  3. Interquartile Range (IQR):
    The IQR is the range of the middle 50% of the data, calculated as Q3Q1Q_3 - Q_1 (length of the box).

    • Class A: Box length is visibly larger than Class B.
    • Class B: Box length is smaller.
      Class A has a larger IQR.
  4. Median Test Score:
    The median is represented by the vertical line inside the box.

    • Class A: Median ≈ 75.
    • Class B: Median ≈ 70.
      Class A has a higher median test score.

Final Answers:

(a) Class B had a smaller range of test scores.
(b) Class A had the highest test score.
(c) Class A had test scores with a larger interquartile range (IQR).
(d) Class A had a higher median test score.

Let me know if you would like further clarification on any part!


Related Questions:

  1. How do you calculate the range and IQR from box-and-whisker plots?
  2. What does the median indicate about the data distribution?
  3. Why is the IQR useful for understanding data spread?
  4. How would outliers affect a box-and-whisker plot?
  5. Can two boxplots have the same median but different IQRs? Why?

Tip:

The interquartile range (IQR) is resistant to outliers, unlike the range. This makes it more reliable for measuring data spread when extreme values are present.

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Math Problem Analysis

Mathematical Concepts

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

Formulas

Range = Maximum - Minimum
IQR = Q3 - Q1

Theorems

The range is the difference between the minimum and maximum data points.
The median splits the data into two equal halves.
The interquartile range (IQR) measures the spread of the middle 50% of data.

Suitable Grade Level

Grades 6-8