Math Problem Statement
Solution
The correct answer is:
"A value chosen randomly from the data set will typically be contained in the interval [μ - σ, μ + σ]."
Explanation:
- For a dataset with mean μ and standard deviation σ, about 68% of the data values typically fall within one standard deviation from the mean, i.e., in the interval [μ - σ, μ + σ].
- This follows from the empirical rule (68-95-99.7 rule) for normal distributions, which describes how data is distributed in terms of standard deviations from the mean.
Let me know if you have questions or need further clarification!
Here are 5 questions to deepen your understanding:
- What does the standard deviation represent in a data set?
- How would the interval change for 95% of the data instead of 68%?
- How can this interval differ for non-normally distributed data?
- Can a value outside the interval [μ - σ, μ + σ] occur? If so, how often?
- What happens to the interval [μ - σ, μ + σ] when the standard deviation is very large?
Tip: Always check whether the distribution is normal when applying the empirical rule!
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Math Problem Analysis
Mathematical Concepts
Statistics
Empirical Rule
Standard Deviation
Formulas
Interval [μ - σ, μ + σ] covers approximately 68% of data for a normal distribution
Theorems
Empirical Rule (68-95-99.7 Rule)
Suitable Grade Level
Grades 9-12
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