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 
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; 
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  


Least squares line


Standard error of estimate


Pearson productmoment correlation
coefficient


Coefficient of determination r ^{2} 

Confidence interval for y y_{p}  E < y < y_{p} + E where y_{p} is the predicted y value for x


Spearman Rank correlation coefficient
