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SOME STATISTICS FORMULAS
| FREQUENTLY USED FORMULAS | n = sample size; N = population size |
| Sample mean
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| Population mean
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| Sample standard deviation
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| Population standard deviation
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| Sample mean for a frequency
distribution
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| Sample standard deviation for
a frequency distribution
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| Sample coefficient of
variation
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| Range = Largest data value - smallest data value | |
| Standard z value
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| Original x value
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| Central limit theorem
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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
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| General multiplication rules
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| 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
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| Combination rule
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| Mean of a discrete probability distribution
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| Standard deviation of a discrete probability
distribution
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| BINOMIAL DISTRIBUTION FORMULAS | where r = number of
successes; |
| Formula for a binomial
probability distribution
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| Mean for a binomial
distribution
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| Standard deviation for a
binomial distribution
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CONFIDENCE INTERVALS |
Confidence interval for a mean (large samples)
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| Confidence interval for a mean (Small
samples)
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| Confidence interval for a proportion
(where np > 5 and nq > 5)
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| SAMPLE SIZE |
| Sample size for estimating means
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| Sample size for estimating proportions
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| REGRESSION AND CORRELATION | |
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| Least squares line
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| Standard error of estimate
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| Pearson product-moment correlation
coefficient
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| Coefficient of determination r 2 |
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| Confidence interval for y yp - E < y < yp + E where yp is the predicted y value for x
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| Spearman Rank correlation coefficient
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