SUMMARY
Chebychev's Theorem is applied to analyze the eruption durations of Old Faithful Geyser, with a sample size of n = 32, a mean duration of 3.32 minutes, and a standard deviation of 1.09 minutes. The theorem states that for any k standard deviations from the mean, at least (1 - 1/k²) of the data falls within that range. To determine how many eruptions lasted between 1.14 minutes and 5.5 minutes, k is calculated as approximately 2, leading to at least 75% of eruptions, or 24 eruptions, falling within this interval.
PREREQUISITES
- Understanding of Chebychev's Theorem
- Basic statistics concepts: mean and standard deviation
- Ability to calculate standard deviations from a mean
- Familiarity with sample size implications in statistical analysis
NEXT STEPS
- Study the applications of Chebychev's Theorem in various statistical contexts
- Learn how to calculate confidence intervals using standard deviations
- Explore the differences between Chebychev's Theorem and the Empirical Rule
- Investigate the significance of sample size in statistical inference
USEFUL FOR
Students in statistics, educators teaching probability theory, and researchers analyzing data distributions using Chebychev's Theorem.