SOME STATISTICS FORMULAS



SOME STATISTICS FORMULAS

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|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 |

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|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 |

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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; |

| |p = probability of success;   q = 1 - p |

|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 |

|In all these formulas |

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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 |

|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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