Chi squared test for goodness of fit
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Medians, quartiles and percentiles.
The median of a probability distribution is that value that divides the distribution into two halves. That is, it is the value of the variable X such that the cumulative probability of X up to that value is ½. Let M denote the median value. Then, if F(t) is the cumulative distribution function for X, then [Equation.] If f(x) is the probability density function for X, then [Equation.] Example A random variable X has probability density function given by [Equation.] Find the cumulative distribution function for X and find the median of x. [Equation. [Equation.] [Equation.] Hence [Equation.] For the median we require F(m) = ½ [Equation.] The first and third quartiles are the value t and t such that [Equation.] A percentile is a value of t such that F(t) is equal to a given percentage of the cumulative distribution.
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Contents of
Chi squared test for goodness of fit
1 Medians, quartiles and percentiles.
2 Modelling of theoretical distributions to given data and the Chi squared test for goodness of fit
3 Approximation by the chi squared test
4 Example of modelling using the chi squared test for goodness of fit
5 Cumulative distribution function.
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