stats 108

 

 

Equations for Midterm 1  

Outliers If data follow a normal distribution, then any points that are further than 3 standard deviations away from the mean are considered outliers, x < μ ‐ 3σ or  x > μ + 3σ  For any non-normal distribution or distribution unknown,

any x < Q1-1.5*IQR or any x > Q3+1.5*IQR is considered an outlier

Population variance = σ2 =

Population standard deviation = σ = √

Sample variance = s2 =

Sample standard deviation = s = s2

Range= Largest value-smallest value Five number summary: min, Q1,median,Q3, max IQR, Interquartile Range = Q3 – Q1 Conditional probability

P( A | B)  P( A B)

P(B)

A and B are independent events if: P(A|B)=P(A) or P(B|A)=P(B) or P(A∩B)=P(A)*P(B) First property of probability   0 ≤ P (Ei) ≤ 1, 0 ≤ P (A) ≤ 1  Second property of probability ΣP (Ei) = 1 Two characteristics of a probability distribution 1. 0 ≤ P (x) ≤ 1 2. ΣP (x) = 1 Addition Rule P(A B) = P(A) + P(B) – P(A∩B) Combinations Notation   nCx =

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Permutations Notation    nPx =  !

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