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1. 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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