Asked by Akilah Walcott on Jun 05, 2024
Verified
The mean and variance of a sample of n = 25 measurements are 80 and 100, respectively. Explain in detail how to use Tchebysheff's Theorem to describe the distribution of measurements.
Variance
An index of variability in a set of data, established by taking the average squared deviation from the mean.
Tchebysheff's Theorem
A theorem that states for any real numbers k > 1, at least (1-1/k^2) of the data values fall within k standard deviations of the mean for any distribution.
- Master the employment and boundaries of statistical methodologies (Empirical Rule, Tchebysheff's Theorem) in the characterization of data.
- Employ the Empirical Rule and Tchebysheff's Theorem in both theoretical frameworks and real-world situations.
- Explain the computation and significance of variance and standard deviation in data analysis.
Verified Answer
AS
avtar singhJun 10, 2024
Final Answer :
The distribution of measurements is centered about 80, and Tchebysheff's Theorem states: At least 3/4 of the 25 measurements lie within 2 SD of the mean, that is, between 60 to 100. At least 8/9 or of the measurements lie within 3 SD of the mean, that is, between 50 to 110.
Learning Objectives
- Master the employment and boundaries of statistical methodologies (Empirical Rule, Tchebysheff's Theorem) in the characterization of data.
- Employ the Empirical Rule and Tchebysheff's Theorem in both theoretical frameworks and real-world situations.
- Explain the computation and significance of variance and standard deviation in data analysis.