Math Problem Statement

Use this box and whisker plot to answer the following questions. What is the overall median of the data? What is the least value of the second group? What is the greatest value of the third group?

Solution

Based on the box and whisker plot shown in the image, we can extract the following information:

  • Median (Q2): The median is represented by the vertical line in the box. The value for the median appears to be 45.5.
  • Least Value of the Second Group: The second group lies between the first quartile Q1Q_1 and the median Q2Q_2. The least value for this group would be at 34.7, the value of Q1Q_1.
  • Greatest Value of the Third Group: The third group lies between Q2Q_2 and Q3Q_3, and the greatest value of this group would be at 63.6, which is the value of Q3Q_3.

Here's how you can fill out the answers in the boxes:

  • Median = 45.5
  • Least Value = 34.7
  • Greatest Value = 63.6

Would you like further explanations on how to read box and whisker plots or the meaning of quartiles?

Here are 5 related questions to deepen your understanding:

  1. How are quartiles calculated from raw data?
  2. What does the interquartile range (IQR) represent in a box and whisker plot?
  3. How do outliers affect a box plot?
  4. What is the significance of the whiskers in a box plot?
  5. Can a box plot be used to identify skewness in data?

Tip: In box plots, the line in the middle of the box always represents the median, which splits the data into two equal halves.

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Math Problem Analysis

Mathematical Concepts

Box and Whisker Plot
Quartiles
Median
Range

Formulas

Median = Q2 (Middle value of the dataset)
Interquartile Range (IQR) = Q3 - Q1

Theorems

Quartile Theorem
Central Tendency Theorem

Suitable Grade Level

Grades 6-8