Probability chebychev theorem

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kaylor koh

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Sep 20, 2009
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Hello
I have a question on Chebychev's theorem.
1.Given a distribution of 1567 numbers. The mean is 100 and the standard deviation is 10. According to Chebychev's theorm, AT LEAST 8/9 of the values in the distribution must fall between 2 numbers. What are the 2 numbers.
I have absolutly no clue about this question, please help.

Thank you :D
 
According the Chebyshev's theorem, at least 88.9% of the data lie within 3 standard deviations of the mean.

Generally, the theorem says the portion of any data set lies within k standard deviations from the mean is at least \(\displaystyle 1-\frac{1}{k^{2}}, \;\ k>1\)

\(\displaystyle 1-\frac{1}{3^{3}}=\frac{8}{9}, \;\ where \;\ k=3\)

3 standard deviations from the mean. Your SD is 10 and the mean is 100.

See now?.
 
galactus said:
According the Chebyshev's theorem, at least 88.9% of the data lie within 3 standard deviations of the mean.

Generally, the theorem says the portion of any data set lies within k standard deviations from the mean is at least \(\displaystyle 1-\frac{1}{k^{2}}, \;\ k>1\)

\(\displaystyle 1-\frac{1}{3^{3}}=\frac{8}{9}, \;\ where \;\ k=3\)

3 standard deviations from the mean. Your SD is 10 and the mean is 100.

See now?.
Click to expand...

I understand the 3 standard deviations fromthe mean, but how do I find the 2 number?Thank you
 
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