Statistical Formulas

Mode

1. All classes have the same width.

Modes of Grouped Data

2. The classes have different width.

Height of a Histogram Formula

Statistical Mode Formula


Median

Formula of the Median


Arithmetic Mean

Arithmetic Mean Formula

Arithmetic Mean Formula

Grouped Data

Arithmetic Mean of Grouped Data Formula

Arithmetic Mean of Grouped Data Formula


Quartiles

Calculation of Quatiles for Grouped Data

Deciles

Deciles Formula


Percentiles

Percentile Formula


Average Deviation

Average Deviation Formula

Average Deviation Formula

Grouped Data

Average Deviation for Grouped Data Formula

Average Deviation for Grouped Data Formula


Variance

Variance FormulaVariance Formula

Variance for Grouped Data FormulaVariance for Grouped Data Formula

Grouped Data

Variance for Grouped Data FormulaVariance for Grouped Data Formula

Variance for Grouped Data FormulaVariance for Grouped Data Formula


Standard Deviation

Standard Deviation FormulaStandard Deviation Formula

Standard Deviation for Grouped Data FormulaStandard Deviation for Grouped Data Formula

Grouped Data

Standard Deviation for Grouped Data FormulaStandard Deviation for Grouped Data Formula

Standard Deviation for Grouped Data FormulaStandard Deviation for Grouped Data Formula


Coefficient of Variation

Coefficient of Variation Formula


Standard Scores

Standard Score Formula


Covariance

Covariance Formula

Covariance Formula


Linear Correlation Coefficient

Linear Correlation Coefficient Formula


Linear Regression

Line of Regression of y on x

Line of Regression of y on x Formula

Line of Regression of x on y

Line of Regression of x on y Formula


Central Limit Theorem

Central Limit Theorem Formula

N(0, 1)Central Limit Theorem Formula


Combinatorics Formulas

Factorial of a Natural Number

Factorial of a Natural Number

Factorial of a Natural Number


Permutations

Permutations

Permutations and Factorials

If k equals n:

Permutations


Permutations with Repetition

Permutations with Repetition

Permutations with repetition of n elements are permuations where the first element is repeated a times, the second b times, the third c times, ...

n = a + b + c + ...

Permutations with Repetition


Circular Permutations

Circular Permutations


Combinations

Combinations

Combinations and Factorials


Combinations with Repetition

Combinations with Repetition


Probability Formulas

0 ≤ p(A) ≤ 1

p(S) = 1

Probabilidad del suceso imposible

Probabilidad del suceso contrario


Probability Formula

Probability Formula


Addition Rule

If A intersección B ≠ Conjunto vacio.

p(A unión B) = p(A) + p(B) − p(A intersección B)

p(A unión B unión C) = p(A) + p(B) + p(C) − p(A intersección B) − p(A intersección C) − p(B intersección C) + p(A intersección B intersección C)


Multiplication Rule

Independent Events

p(A intersección B) = p(A) · p(B)

Dependent Events

p(A intersección B) = p(A) · p(B|A)


Conditional Probability

Conditional Probability Formula

Independent Events

p(A|B) = p(A)

Dependent Events

p(A|B) ≠ p(A)


Law of Total Probability

p(B) = p(A1) · p(B|A1) + p(A2) · p(B|A2 ) + ... + p(An) · p(B|An )


Bayes' Theorem

Bayes' Theorem Formula


Expected Value

Expected Value Formula


Variance of a Discrete Random Variable

Variance of a Discrete Random Variable

Standard Deviation of a Discrete Random Variable

Standard Deviation of a Discrete Random Variable


Binomial Distribution

Binomial Distribution Formula

Binomial Coefficient


Normal Approximation to the Binomial

Normal Approximation to the Binomial

Normal Approximation to the Binomial




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