Math Problem Statement
The data represent the age of world leaders on their day of inauguration. Find the five-number summary, and construct a boxplot for the data. Comment on the shape of the distribution. 6868 6666 6767 5959
5656 5959 6666 4141 4444 5757 6868 6969 4848 6565 6767
Solution
Five-Number Summary:
- Minimum: 41
- First Quartile (Q1): 56
- Median (Q2): 65
- Third Quartile (Q3): 67
- Maximum: 69
Boxplot Analysis:
- The distribution appears to be slightly left-skewed, as the whisker on the lower end is longer, indicating more variation in the younger ages.
- Most of the ages (between Q1 and Q3) are clustered in the upper half (56-69), suggesting that world leaders tend to be older.
Let me know if you'd like further details or have any questions.
Here are 5 related questions:
- What is the interquartile range (IQR) of the data?
- How would an outlier be detected in this boxplot?
- What does the skewness of the data tell us about the age of leaders?
- Could a histogram provide additional insights about this distribution?
- How would the median age of leaders compare to the mean age?
Tip: The median is often a better measure than the mean when dealing with skewed data, as it isn't influenced by extreme values.
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Five-Number Summary
Boxplot
Distribution Shape
Formulas
Five-number summary: Min, Q1, Median (Q2), Q3, Max
Interquartile Range (IQR): Q3 - Q1
Theorems
Concept of Quartiles and Median
Boxplot Analysis for Distribution Shape
Suitable Grade Level
Grades 9-12
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