Math Problem Statement
Suppose the accompanying data are median ages (in years) for residents of each of the 50 U.S. states and the District of Columbia (DC) in a particular year.
Use these data to calculate the values (in years) in the five-number summary.
smallest observation? lower quartile? median? upper quartile? largest observation?
Solution
The five-number summary for the median ages of the 50 U.S. states and the District of Columbia (DC) is as follows:
- Smallest observation: 29.0 years
- Lower quartile (Q1): 35.85 years
- Median (Q2): 38.5 years
- Upper quartile (Q3): 40.85 years
- Largest observation: 46.6 years
Would you like further details or explanations?
Here are 5 related questions:
- What is the interquartile range (IQR) for these data?
- How could outliers be identified using this five-number summary?
- How would the five-number summary change if another state had an extremely high or low median age?
- What statistical insights can be drawn from the distribution of median ages across the states?
- What are potential reasons for variations in median age among different states?
Tip: The five-number summary is a powerful way to quickly understand the spread and central tendency of a dataset.
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Math Problem Analysis
Mathematical Concepts
Statistics
Descriptive Statistics
Five-Number Summary
Formulas
Q1 = (n+1)/4
Q2 (Median) = (n+1)/2
Q3 = 3(n+1)/4
Theorems
Five-Number Summary
Quartiles
Suitable Grade Level
Grades 9-12
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