Asked by Karim Moukrem on Jun 07, 2024

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​Statements about the proportion of data values that must be within a specified number of standard deviations of the mean can be made using

A) ​Chebyshev's theorem.
B) The empirical rule.
C) ​A five-number summary.
D) Percentiles.

Chebyshev's Theorem

A statistical rule that gives a minimum proportion of observations that fall within a specified number of standard deviations from the mean, for any distribution.

Empirical Rule

A statistical rule stating that for a normal distribution, nearly all data will fall within three standard deviations of the mean.

Five-number Summary

A descriptive statistic that provides a quick overview of a data set's distribution, consisting of the minimum, first quartile, median, third quartile, and maximum.

  • Use concepts of statistical analysis to examine variability in data between different samples or populations.
  • Differentiate among various indicators of variability and understand their applicability.
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Nikka Villanueva HilarioJun 10, 2024
Final Answer :
A
Explanation :
Chebyshev's theorem is a general rule that can be applied to any data set, regardless of its shape or distribution. It states that for any data set, at least 1 - 1/k^2 of the data values must be within k standard deviations of the mean, where k is any positive integer greater than 1. This makes it a more versatile tool for making statements about the spread of data than the empirical rule, which only applies to bell-shaped distributions. The five-number summary and percentiles are useful for summarizing and comparing data sets, but they do not provide information about the proportion of values within a certain distance from the mean like Chebyshev's theorem does.