Asked by Tenica Colbert on Sep 23, 2024
Verified
Chebysheff's Theorem states that the percentage of measurements in a data set that fall within three standard deviations of their mean is:
A) 75%.
B) at least 75%.
C) 89%.
D) at least 88.9%.
Chebysheff's Theorem
A statistical theorem that provides a minimum probability for the distribution of values within k standard deviations from the mean for any data set, regardless of the distribution's shape.
Standard Deviations
A measure of the amount of variation or dispersion of a set of values from the average.
- Comprehend the principle and utilization of Chebysheff's Theorem.
Verified Answer
MJ
maulik jivani4 days ago
Final Answer :
D
Explanation :
Chebyshev's Theorem guarantees that for any distribution, at least 1−1k21 - \frac{1}{k^2}1−k21 of the data within kkk standard deviations from the mean. For k=3k=3k=3 , this gives at least 1−132=1−19=89=88.9%1 - \frac{1}{3^2} = 1 - \frac{1}{9} = \frac{8}{9} = 88.9\%1−321=1−91=98=88.9% .
Learning Objectives
- Comprehend the principle and utilization of Chebysheff's Theorem.