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Formula list in descriptive statistics, probability, inferential statistics, mean and proportion.
Typology: Cheat Sheet
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(I) Descriptive Statistics
x¯ =
Σ xi
n
sx =
n − 1
Σ (xi − x¯)^2
sp =
(n 1 − 1)s 2 1 + (n^2 −^ 1)s
2 2 (n 1 − 1) + (n 2 − 1)
yˆ = b 0 + b 1 x
b 1 =
Σ (xi − x¯)(yi − y¯)
Σ (xi − ¯x)^2
b 0 = ¯y − b 1 x¯
r =
n − 1
xi − x¯
sx
yi − y¯
sy
b 1 = r
sy
sx
sb 1 =
Σ (yi − yˆi)^2
n − 2 √ Σ (xi − x¯)^2
(II) Probability
E(X) = μx = Σ xipi
Var(X) = σ^2 x = Σ (xi − μx)^2 pi
If X has a binomial distribution with parameters n and p, then:
P (X = k) =
n
k
p k (1 − p) n−k
μx = np
σx =
np(1 − p)
μpˆ = p
σpˆ =
p(1 − p)
n
If ¯x is the mean of a random sample of size n from an infinite
population with mean μ and standard deviation σ, then:
μx¯ = μ
σ¯x =
σ √ n
