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

Answers

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.

Chebyshev’s theoremsays that for any set of observations, theproportionof values that lie within kstandard deviationsof themeanis 1 – 1/k².## What do you mean by standard deviation?

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