Math Problem Statement

Find the 5-number summary for the data shown using the interpolation method.

Solution

The five-number summary for the data set is as follows:

  • Minimum: 4.2
  • First Quartile (Q1): 8.6
  • Median: 18.2
  • Third Quartile (Q3): 22.525
  • Maximum: 29.1

Would you like more details or have any questions?

Here are 5 related questions:

  1. How do you calculate quartiles manually?
  2. What does the five-number summary tell us about the data distribution?
  3. How is the interpolation method used in determining quartiles?
  4. What are outliers, and how can they be detected using the five-number summary?
  5. How does the five-number summary differ from a box plot?

Tip: The interquartile range (IQR), which is Q3 - Q1, is useful for detecting outliers in data sets.

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Math Problem Analysis

Mathematical Concepts

Statistics
Quartiles
Five-number summary
Interpolation

Formulas

Quartile formula for Q1: (n+1)/4
Quartile formula for Q3: 3(n+1)/4
Interpolation formula for quartiles

Theorems

Interpolation method
Quartile calculation theorem

Suitable Grade Level

Grades 9-12