AP Statistics Formula Sheet
AP Statistics Formula Sheet
(I) Descriptive Statistics
x
xi
n
sx
1 n1
(xi x)2
sp
(n1 1)s12 (n2 1)s22 (n1 1) (n2 1)
y^ bo b1x
b1
(xi x)(yi y) (xi x)2
bo y b1x
r1 n1
xi x sx
yi y sy
b1
r sy sx
( yi y^i )2
sb1
n2 (xi x)2
(II) Probability
P(A B) = P(A) + P(B) ? P(A B) P(A B)
P(A | B) =
P(B)
E(X) = x
xi pi
Var(X) =
2 x
( xi
x )2 pi
If X has a binomial distribution with Parameters n and p, then:
nk
n?k
P(X = k) = p (1 ? p)
k
?x = np
x np(1 p) p p^
p(1 p)
p^
n
If x is the mean of a random sample of size n
from an infinite population with mean ? and standard deviation , then:
x
x n
(III) Inferential Statistics
Standardized test statistic:
statistic ? parameter standard deviation of statistic
Confidence interval: statistic ? (critical value) ? (standard deviation of statistic)
Single?Sample
Statistic Sample Mean Sample Proportion
Standard Deviation Of Statistic
n p(1 p)
n
Statistic
Two?Sample
Standard Deviation Of Statistic
Difference of sample means
2
2
1
2
n1 n2
Special case when 1 2 11 n1 n2
Difference of sample proportions
p1 (1 p1 ) p2 (1 p2 )
n1
n2
Special case when p1 = p2 11
p(1 p) n1 n2
(observed exp ected)2
Chi-square test statistic =
exp ected
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