Summary AP Statsitics Cheat Sheet

AP STATISTICS FORMULAS


Descriptive Statistics


n
∑i=1 ∑ (x − μ)2
x̄ = σ = = Population
n N

IQ R = Q3 − Q1
∑ (x − x̄)2
Q1 − (1.5 ⋅ IQ R) = Lower Outlier s= = Sample
n−1
Q3 + (1.5 ⋅ IQ R) = Higher Outlier


x−μ
z= Correlation Coefficient = −1 ≤ r ≤ 1
σ



n − 1 ∑ ( sx )( sy ) ( sx )
1 xi − x̄ yi − ȳ sy
r = ŷ = bx + a b=r a = ȳ − b x̄




∑ (yi − yî )2
Residual = yi − yî Root-mean-square deviation = R2 = 0 ≤ r 2 ≤ 1
n−2


Probability and Distributions


P(A ∩ B)
P(A ∪ B) = P(A) + P(B) − P(A ∩ B) P(A∖B) =
P(B)


Discrete random variable, X

E(xi − μx )2 ⋅ P(xi ) =
∑
μx = E(X ) = xi ⋅ P(xi ) σx = Var(X )

E(X + Y ) = E(X ) + E(Y ) Var(X + Y ) = Var(X ) + Var(Y )
2
σx−y = σx2 + σy2

, If X has a binomial distribution with parameters n and p, then:


(x)
n
P(X = x) = p x(1 − p)n−x where x = 0, 1, 2 ,3, …, n


μx = np Var(X ) = np(1 − p) σx = np(1 − p) = Var(X )


If X has a geometric distribution with parameter p, then:


(x)
n
P(X = x) = p x (1 − p)n−x where x = 0, 1, 2, 3, …, n


1 1−p
μx = σx =
p p

Sampling Distributions and Inferential Statistics


Random Variable Parameters of Sampling Distribution Standard Error* of
Sample Statistic




̂ − p)̂
p(1
For one population: p̂ μp̂ − p sp̂ =
n
p(1 − p)
σp̂ =
n



p1(1 − p1) p2(1 − p2 )
For two populations: μp1̂ −p̂2 = μp1̂ − μp̂2 sp1̂ −p̂ 2 = +
n1 n2
p1̂ − p2̂
p1(1 − p1) p2(1 − p2 )
σp1̂ −p̂ 2 = + when p1 = p2 is assumed:
n1 n2



( n1 n 2 )
1 1
sp1̂ −p̂ 2 = pĉ (1 − pĉ ) +

X1 + X2
where pĉ =
n1 + n 2