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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

eqn157.gif (380 bytes)

General multiplication rules

eqn158.gif (484 bytes)
eqn159.gif (482 bytes)

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

eqn160.gif (337 bytes)

Combination rule

eqn161.gif (362 bytes)

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

eqn162.gif (484 bytes)

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