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

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 thought on “Chebyshev’s theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the m”

  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:
    #SPJ1

    Reply

Leave a Comment