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AP Statistics Formula Sheet
(I) Descriptive Statistics
2
2
1
1
(^12)
1
1 2
2 2 2
2 1 1
2
1 x x
n
y y
s
s
s b r
s
y y
s
x x
n
r
b y bx
x x
x x y y b
y b bx
n n
n s n s s
x x n
s
n
x x
i
i i
b
x
y
y
i
x
i
o
i
i i
o
p
x i
i
(II) Probability
P(A B) = P(A) + P(B) – P(A ∩ B)
P(A | B) =
P B
P A B
E(X) = x xipi
Var(X) = x xi x pi
2 2
If X has a binomial distribution with
Parameters n and p , then:
P(X = k ) =
k
n
p
k
(1 – p )
n–k
μx = np
x np (^1 p )
n
p p
p
p
p
ˆ
ˆ
If x is the mean of a random sample of size n
from an infinite population with mean μ and
standard deviation σ, then:
x
n
x
(III) Inferential Statistics
Standardized test statistic: statistic – parameter
standard deviation of statistic
Confidence interval: statistic ± (critical value) • (standard deviation of statistic)
Single–Sample
Statistic Standard Deviation
Of Statistic
Sample Mean
n
Sample Proportion
n
p ( 1 p )
Two–Sample
Statistic Standard Deviation
Of Statistic
Difference of
sample means
2
2 2
1
2 1
n n
Special case when 1 2
1 2
n n
Difference of
sample proportions
2
2 2
1
1 (^11 ) (^1 )
n
p p
n
p p
Special case when p 1 = p 2
1 2
n n
p p
Chi-square test statistic =
ected
observed ected
exp
( exp )
2
