Math Problem Statement

Based on the boxplot above, identify the five-number summary.

Solution

To identify the five-number summary from the boxplot, we need to extract the following key data points:

  1. Minimum: The smallest value.
  2. First Quartile (Q1): The 25th percentile.
  3. Median: The middle value (50th percentile).
  4. Third Quartile (Q3): The 75th percentile.
  5. Maximum: The largest value.

Based on the boxplot provided:

  • Minimum: The smallest value is at 7.
  • First Quartile (Q1): The first quartile is at 10.
  • Median: The median (middle value) is at 13.
  • Third Quartile (Q3): The third quartile is at 17.
  • Maximum: The largest value is at 20.

The five-number summary is:

  • Minimum: 7
  • Q1: 10
  • Median: 13
  • Q3: 17
  • Maximum: 20

Would you like further details or clarification?

Here are 5 questions to expand your understanding:

  1. How is the interquartile range (IQR) calculated using the five-number summary?
  2. What does the shape of the boxplot tell us about the distribution of the data?
  3. How does the presence of outliers affect the five-number summary?
  4. What is the significance of the median in the boxplot?
  5. How do you interpret the difference between Q3 and Q1?

Tip: The larger the box (between Q1 and Q3), the more spread out the middle 50% of the data.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Five-number summary
Boxplot

Formulas

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Theorems

Five-number summary theorem
Percentiles

Suitable Grade Level

Grades 7-10