AP Statistics: FORMULAS AND TABLES
(I) Descriptive Statistics
i
3x
x =
n
1
xi
s = 3 (x โ x )2
r n โ 1
11 22
(n โ 1)s + (n โ 1)s
22
p
s =
12
r (n โ 1) + (n โ 1)
01
yห = b + bx
ii
3(x โ x )(y โ y )
1
b =
i
3(x โ x )2
01
b = y โ bx
ii
1 x โ x y โ y
r = j
xy
n โ 1 ๎ s ๎๎ s ๎
y
s
1
b = r
x
s
ii
3(y โ yห )2
= r n โ 2
i
3(x โ x )2
p
(II) Probability
P(A c B) = P(A) + P(B) โ P(A 1 B)
P(A 1 B)
P(A*B) = P(B)
xii
E(X) = : = 3x p
xixi
Var(X) = F = 3 (x โ :) p
22
If X has a binom ial distribution with parameters
n and p, then:
n
P(X = k) = p (1 โ p)
k n โ k
๎ k ๎
x
: = np
x
F = /np(1 โ p)
pห
: = p
p(1 โ p)
pห
F =
q n
If x is the mean of a random sample of size n
from an infinite population with mean : and
standard deviation F, then:
(III) Inferential Statistics
Standardized statistic โ parameter
test statistic: standard deviation of statistic
Confidence interval:
statistic ยฑ (critical value) โข (standard deviation of statistic)
Single-Sample
Statistic Standard Deviation
of Statistic
Sample Mean F
/n
Sample Proportion
p(1 โ p)
r n
Two-Sample
Statistic Standard Deviation
of Statistic
Difference of
sample means
12
F F
22
+
12
r n n
12
Special case when F = F
1 1
F +
12
r n n
Difference of
sample proportions
1122
p(1 โ p) p(1 โ p)
+
12
r n n
12
Special case when p = p
1 1
pp(1 โ p) +
12
r n n
(observed โ expected)
2
Chi-square test statistic =
' expected
