Download AP Statistics Formula Sheet

AP Statistics Formula Sheet
(I) Descriptive Statistics
x
x
i
n
sx 
1
( xi  x ) 2

n 1
sp 
(n1  1) s12  (n2  1) s22
(n1  1)  (n2  1)
yˆ  bo  b1 x
 ( x  x )( y  y )
 (x  x)
b1 
i
i
2
i
bo  y  b1 x
r
 xi  x  yi  y 
1




n  1  s x  s y 
b1  r
sy
sx
 ( y  yˆ )
i
sb1 
2
i
n2
 ( xi  x ) 2
(II) Probability
P(A  B) = P(A) + P(B) – P(A ∩ B)
P(A | B) =
E(X) =
P( A  B)
P( B)
 x   xi p i
 x2   ( xi   x ) 2 pi
Var(X) =
If X has a binomial distribution with
Parameters n and p, then:
n k
n–k
P(X = k) =   p (1 – p)
k
 
µx = np
 x  np(1  p)
 pˆ  p
p (1  p )
n
 pˆ 
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  
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
Standard Deviation
Of Statistic

n
p (1  p )
n
Sample Mean
Sample Proportion
Two–Sample
Statistic
Standard Deviation
Of Statistic
 12
Difference of
sample means
n1

 22
n2
Special case when  1   2

Difference of
sample proportions
1 1

n1 n2
p1 (1  p1 ) p 2 (1  p2 )

n1
n2
Special case when p1 = p2
p(1  p)
(observed  exp ected ) 2
Chi-square test statistic = 
exp ected
1 1

n1 n2