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:
- Minimum: The smallest value.
- First Quartile (Q1): The 25th percentile.
- Median: The middle value (50th percentile).
- Third Quartile (Q3): The 75th percentile.
- 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:
- How is the interquartile range (IQR) calculated using the five-number summary?
- What does the shape of the boxplot tell us about the distribution of the data?
- How does the presence of outliers affect the five-number summary?
- What is the significance of the median in the boxplot?
- 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