Stats Symbols & Concepts: Pop. vs Sample, Mean, Variance, Proportion, CLT, & Normal Approx, Study notes of Data Analysis & Statistical Methods

Download Stats Symbols & Concepts: Pop. vs Sample, Mean, Variance, Proportion, CLT, & Normal Approx and more Study notes Data Analysis & Statistical Methods in PDF only on Docsity! Definition of some symbols Please note the similarities and differences N = Population size = Number of elements in the population1 N = Sample size = Number of units in the sample  = Mean of the population (of X’s = X ) 2 = E(X) ( ) ( ) all x X X xP X x if X is a discrete rv xf x dx if X is a continuous rv              X = Mean of the sample from the population of X’s = 1 1 n i i X n   X = Mean of the population of sample means = E( X ) [ =  by rule 1] ( ) ( ) all x X X xP X x if X is a discrete rv xf x dx if X is a continuous rv            2 X =Variance of the population of X’s = 2 X 2 2 2 _ ( ) ( ) if X is a discrete rv ( ) ( ) if X is a continuous rv X all x X X X x P X x x f x dx                2 X = Variance of the population of sample means [ = 2 X n  by Rule 2]. 2 2 2 _ ( ) ( ) if X is a discrete rv ( ) ( ) if X is a continuous rv X all x X X X x P X x x f x dx                 = Proportion of “Success”s in the population. = (Number of “Success”s in the population) / N p = Proportion of “Success”s in the sample = (Number of “Success”s in the sample) / n p = Mean of the population of sample proportions = E(p) =  by rule 6 2 p = Variance of the population of sample proportions = (1 ) / n  by rule 9. 1 Assumed to be infinity in many theoretical studies, but finite in almost all real life problems. 2 The subscript indicating the population (X, Y, etc.) will be dropped when there is no possible confusion.