Formulas and Tables for AP Statistics
I. Descriptive Statistics
1i
i
x
xx
nn
∑
=∑=
( ) ( )
2
2
1
11
i
xi
xx
s xx
nn
∑−
= ∑− =
−−
ˆ
y a bx= +
y a bx= +
1
1
ii
xy
xxyy
rn ss
−−
= ∑
−
y
x
br
s
=
s
II. Probability and Distributions
( ) ( ) ( ) ( )
PA B PA PB PA B∪= + − ∩
( ) ( )
( )
|PA B
PAB PB
∩
=
Probability Distribution Mean Standard Deviation
Discrete random variable, X
µ
=
X
E
(
X
)
= ∑ xP
i
(
x
)
i
σ
X
=∑−x
iX
Px
i
µ
( )
2
( )
If 𝑋𝑋 has a binomial distribution
with parameters n and p, then:
n
PX
(
=x
)
=p
x
(
1−p
)
nx−
x
where x=0, 1, 2, 3, ,n
µ
=
X
np
σ
=
Xnp
(
1−p
)
If 𝑋𝑋 has a geometric distribution
with parameter p, then:
PX
(
=x
)
=
(
1−p
)
x−1
p
where
x=1, 2, 3,
1
µ
=
X
p
1−p
σ
=
X
p
III. Sampling Distributions and Inferential Statistics
Standardized test statistic:
statistic parameter
standard error of the statistic
−
Confidence interval:
( )( )
statistic critical value standard error of statistic±
Chi-square statistic:
( )
2
observed expected
expected
χ
−
=
∑
2
AP Statistics 2020 Formulas and Tables Sheet
