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 Sierra College Mathematics Department

SOME STATISTICS FORMULAS

 FREQUENTLY USED FORMULAS n = sample size; N = population size Sample mean Population mean Sample standard deviation Population standard deviation Sample mean for a frequency distribution Sample standard deviation for a frequency distribution Sample coefficient of variation Range = Largest data value - smallest data value Standard z value Original x value Central limit theorem

 PROBABILITY FORMULAS Probability of an event A where f = frequency of occurrence of event n = sample size Probability of the complement of event A P(not A) = 1 - P(A) Multiplication rule for independent events General multiplication rules Addition rule for mutually exclusive events P(A or B) = P(A) + P(B) General addition rule P(A or B) = P(A) + P(B) - P(A and B) Permutation rule Combination rule Mean of a discrete probability distribution Standard deviation of a discrete probability distribution

 BINOMIAL DISTRIBUTION FORMULAS where r = number of successes; p = probability of success;   q = 1 - p Formula for a binomial probability distribution Mean for a binomial distribution Standard deviation for a binomial distribution

 CONFIDENCE INTERVALS Confidence interval for a mean (large samples) Confidence interval for a mean (Small samples) Confidence interval for a proportion (where np > 5 and nq > 5)

 SAMPLE SIZE Sample size for estimating means Sample size for estimating proportions

REGRESSION AND CORRELATION
 In all these formulas
Least squares line

Standard error of estimate

Pearson product-moment correlation coefficient

Coefficient of determination

r 2

Confidence interval for y

yp - E < y < yp + E where yp is the predicted y value for x

Spearman Rank correlation coefficient