Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is?

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19-08-2022
Mathematics

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Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is?

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shivishivangi1679 shivishivangi1679 · Answer 1 · 2022-08-24T11:50:20+02:00

Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is 1 - 1/k².

What do you mean by standard deviation?

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We know that Chebyshev's theorem states that for a large class of distributions, no more than 1/k² of the distribution will be k standard deviations away from the mean.

This means that 1 - 1/k² of the distribution will be within k standard deviations from the mean.

Lets k = 1.8, the amount of the distribution that is within 1.8 standard deviations from the mean is;

1 - 1/1.8² = 0.6914

= 69.14%

Hence, Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is 1 - 1/k².

Learn more about standard deviation and variance:

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