Question

according to chebyshev's theorem, what perpent of the observatioons lie within plus and minus 2.5 standard deviations of the mean

Answer 1

percent of the observations lie within plus and minus 2.5 standard deviations of the mean is 84%

according to Chebyshev's theorem k=2.5

Chebyshev theorem:

The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.

This indicates that 1 - $\frac{1}{k^{2} }$ of the distribution will be close to the mean, or within k standard deviations.

Therefore, 1 - $\frac{1}{k^{2} }$

⇒ 1- $\frac{1}{(2.5)^{2} }$

⇒1-$\frac{1}{6.25}$

⇒$\frac{5.25}{6.25}$

⇒0.84

percent of the observations lie within plus and minus 2.5 standard deviations of the mean is 84%

Learn more about standard deviations here:

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