stat review - Chapter 2 Measures of Location and Spread...

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Chapter 2 Measures of Location and Spread Markov's Inequality (for lists) If the mean of a list of numbers is M , and the list contains no negative number then [fraction of numbers in the list that are greater than or equal to x] ≤ M /x. Chebychev's inequality (for lists) If the mean of a list of numbers is M and the standard deviation of the list is SD, then for every positive number k , [the fraction of numbers in the list that are k × SD or further from M ] ≤ 1/ k 2 . Estimating using the Regression Line For regressing Y on X, (estimate of Y in standard units) = r ×(measured X in standard units) For regressing X on Y, (estimate of X in standard units) = r ×(measured Y in standard units). Residual plots can reveal computational errors A residual plot shows at a glance whether the regression line was computed correctly. If the regression line was computed correctly, the point of averages of the residual plot will be on the x -axis, and the residuals will not have a trend: the correlation coefficient for the residuals and X will be zero. If the residuals have a trend, the slope of the regression line was miscalculated. If the residuals do not have a trend, but the average of the residuals is not zero, the intercept of the regression line was miscalculated. If the residuals have a trend and the average of the residuals is not zero, the slope of the regression line was miscalculated, and the intercept of the regression might also have been miscalculated. Permutations The number of possible permutations (orderings) of k of n things is n P k = n !/( n - k )! ( k must be at least 0 and no larger than n .) Combinations The number of possible combinations of n things taken k at a time (without regard to order) is n ! n
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stat review - Chapter 2 Measures of Location and Spread...

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