Bluman A.G. Elementary Statistics- A Step By Step Approach

Important FormulasChapter 3Data DescriptionMean for individual data:Mean for grouped data: X f • X mnStandard deviation for a sample: X2or s 2 Xs 2X n 1nX nn 1(Shortcut formula)Standard deviation for grouped data:s nf • X 2 m f • X m 2nn 1Range rule of thumb:s range4X XnChapter 4 Probability and Counting RulesAddition rule 1 (mutually exclusive events):P(A or B) P(A) P(B)Addition rule 2 (events not mutually exclusive):P(A or B) P(A) P(B) P(A and B)Multiplication rule 1 (independent events):P(A and B) P(A) P(B)Multiplication rule 2 (dependent events):P(A and B) P(A) P(B A)PA and BConditional probability: PB A PAComplementary events: P( E ) 1 P(E)Fundamental counting rule: Total number of outcomesof a sequence when each event has a differentnumber of possibilities: k 1 k 2 k 3 k nPermutation rule: Number of permutations of n objectstaking r at a time is nP r n!n r!Combination rule: Number of combinations of r objectsn!selected from n objects is n C r n r!r!Chapter 5 Discrete Probability DistributionsMean for a probability distribution: m [X P(X)]Variance and standard deviation for a probabilitydistribution:s 2 [X 2 P(X)] m 2s [X 2 • PX] m 2Expectation: E(X) [X P(X)]n!Binomial probability: PX n X!X! • pX • q nXMean for binomial distribution: m n pVariance and standard deviation for the binomialdistribution: s 2 n p q s n • p • qMultinomial probability:n!PX X 1 !X 2 !X 3 ! . . . X k ! • pX 11 • p X 22 • p X 33 •••p X kkPoisson probability: P(X; l) X 0, 1, 2, . . .Hypergeometric probability:Chapter 6Standard score z X whereThe Normal DistributionMean of sample means: m X mStandard error of the mean: s X nCentral limit theorem formula: z X nChapter 7 Confidence Intervals and SampleSizez confidence interval for means:X z 2n X z2nt confidence interval for means:X s t 2n X s t2nSample size for means: n z2 • where E is theE 2maximum error of estimateConfidence interval for a proportion:ˆp ˆqˆp z2 n p ˆp ˆp ˆq z2 ne XX!PX a C X • b C nXabC norz X Xs