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:

  1. Minimum: 41
  2. First Quartile (Q1): 56
  3. Median (Q2): 65
  4. Third Quartile (Q3): 67
  5. 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:

  1. What is the interquartile range (IQR) of the data?
  2. How would an outlier be detected in this boxplot?
  3. What does the skewness of the data tell us about the age of leaders?
  4. Could a histogram provide additional insights about this distribution?
  5. 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