(BQ) Part 1 book "Elementary statistics - A step by step approach" has contents: The nature of probability and statistics, frequency distributions and graphs, data description, probability and counting rules, discrete probability distributions, the normal distribution, confidence intervals and sample size. | This page intentionally left blank Important Formulas Chapter 3 Data Description ᎐ Mean for individual data: X ϭ ᎐ Mean for grouped data: X ϭ Chapter 5 Discrete Probability Distributions ͚X n ͚ f • Xm n ͙ ͚Θ X Ϫ X Ι 2 nϪ1 ͙ nΘ ͚X 2Ι Ϫ Θ͚XΙ 2 nΘn Ϫ 1Ι (Shortcut formula) sϭ or Standard deviation for grouped data: sϭ ͙ 2 nΘ͚ f • X m Ι Ϫ Θ ͚ f • Xm Ι 2 nΘn Ϫ 1Ι Range rule of thumb: s Ϸ s2 ϭ ͚[X 2 и P(X)] Ϫ m2 s ϭ ͙͚[X 2 • PΘXΙ ] Ϫ m2 Standard deviation for a sample: sϭ Mean for a probability distribution: m ϭ ͚[X и P(X)] Variance and standard deviation for a probability distribution: range 4 n! • pX • q nϪX Ϫ XΙ !X! Mean for binomial distribution: m ϭ n и p Variance and standard deviation for the binomial distribution: s2 ϭ n и p и q s ϭ ͙n • p • q Multinomial probability: n! X X X PΘXΙ ϭ • p X 1 • p2 2 • p3 3 • • • pk k X1!X2!X3! . . . Xk! 1 Binomial probability: PΘXΙ ϭ Θn Poisson probability: P(X; l) ϭ Chapter 4 Probability and Counting Rules Addition rule 1 (mutually exclusive events): P(A or B) ϭ P(A) ϩ P(B) Addition rule 2 (events not mutually exclusive): P(A or B) ϭ P(A) ϩ P(B) Ϫ P(A and B) Multiplication rule 1 (independent events): P(A and B) ϭ P(A) и P(B) Multiplication rule 2 (dependent events): P(A and B) ϭ P(A) и P(B ͉ A) Conditional probability: PΘB Խ AΙ ϭ Expectation: E(X) ϭ ͚[X и P(X)] PΘ A and BΙ PΘ AΙ ᎐ Complementary events: P(E ) ϭ 1 Ϫ P(E) Fundamental counting rule: Total number of outcomes of a sequence when each event has a different number of possibilities: k 1 и k 2 и k 3 и и и k n Permutation rule: Number of permutations of n objects n! taking r at a time is n Pr ϭ Θn Ϫ rΙ ! Combination rule: Number of combinations of r objects n! selected from n objects is n Cr ϭ Θ n Ϫ r Ι !r! X ϭ 0, 1, 2, . . . e Ϫ X where X! Hypergeometric probability: PΘXΙ ϭ a CX • bCnϪX aϩbCn Chapter 6 The Normal Distribution Standard score z ϭ ᎐ XϪ zϭ or XϪX s Mean of sample means: mX ϭ m ͙n ᎐ XϪ Central limit theorem .
