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Statistics LibreTexts

Ch 11.1 Chi-square Distribution

  • Page ID
    15930
  • Ch 11.1  Facts about Chi-square distribution

    Notation for chi-square distribution is  χ2 . It is a distribution with degree of freedom (df = n -1).

    Characteristic of chi-square distribution.

    i) Shape of the distribution is right skew,

    non-symmetrical. There is a different chi-square curve for each df. When df > 90, the chi-square curve approximates the normal distribution.

    Chi square distribution

    ii) mean μ = df (n-1), σ = \( 2 \sqrt{df} \). The mean is located just right of the peak.

    chi-square distribution

    iii) = sum of (n-1) independent, standard normal variable. χ2 is always positive.

    Chi-square distribution calculator:

    http://onlinestatbook.com/2/calculators/chi_square_prob.html

    The calculator can be used to find area to the right of a chi-square value P( χ2 > a)

    Ex. Find probability that χ2 is greater than 31 when

    df = 10.

    Enter chi-square = 31, df = 10, calculate.

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