AP Statistics Formula Tables provide essential formulas and statistical concepts for students preparing for the AP Statistics exam. This resource includes descriptive statistics, probability distributions, and sampling distributions, along with critical values for z, t, and chi-square distributions. Designed for high school students, this reference sheet is ideal for quick reviews and exam preparation. It covers key topics such as standard deviations, confidence intervals, and regression analysis, making it a valuable tool for mastering AP Statistics concepts.

Key Points

  • Includes formulas for descriptive statistics and probability distributions essential for AP Statistics.
  • Covers sampling distributions and critical values for z, t, and chi-square distributions for exam readiness.
  • Provides standard error calculations and confidence interval formulas for statistical analysis.
  • Features a comprehensive overview of binomial and geometric distributions with relevant formulas.
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AP® Statistics
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11 pages
AP® Statistics
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Name: ___________________________________________________
NOTE: You may use any blank space in this booklet for scratch work during the exam. Proctors should collect this
reference information at the conclusion of the exam.
AP
®
Statistics
2026 EXAM REFERENCE INFORMATION
Formulas for AP Statistics
I. Descriptive Statistics
1
i
i
x
xx
nn


2
2
1
11
i
xi
x x
s xx
nn


ˆ
y a bx
y a bx
1
1
ii
xy
x x yy
r
n ss








y
x
s
br
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=⋅
x
ii
Px
()
σμ
X
=
(
x
)
2
iX
−⋅Px
(
i
)
If
X
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
X
np
X
np

1 p
If
X
has a geometric distribution with
parameter
p
, then:
PX
x

1 p
x1
p
where
x 1,2 ,3 ,
1
X
p
1
X
p
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
2
observed expected
expected
χ
−
=
© 2025 College Board
 1AP Statistics
III. Sampling Distributions and Inferential Statistics (continued)
Sampling distributions for proportions:
Random Variable Parameters of Sampling Distribution
Standard Error* of
Sample Statistic
For one population:
p
ˆ
ˆ
p
p

ˆ
1
p
p p
n

ˆ
ˆˆ
1
p
p p
s
n
For two populations:
p
ˆ
12
− p
ˆ
12
ˆˆ
12
pp
p p

12
1 12
ˆˆ
1
1
pp
p pp
n
2

12
1 12 2
ˆˆ
12
ˆ ˆˆ ˆ
11
pp
p pp p
s
nn

When
12
p p
is assumed:
()
12
ˆˆ
12
11
ˆˆ
1
cc
pp
s pp
nn
−

=− +


where
12
12
ˆ
c
X X
p
nn
2
1p
n
Sampling distributions for means:
Random Variable Parameters of Sampling Distribution
Standard Error* of
Sample Statistic
For one population:
X

X
X
n
s
s
X
n
For two populations:
X
12
X
22
12

XX
12
12
X
12
X
nn
12
12
22
12
12
XX
ss
s
nn
Sampling distributions for simple linear regression:
Random Variable Parameters of Sampling Distribution
Standard Error* of
Sample Statistic
For slope:
b
b
b
x
n
,
where

2
i
x
x x
n
1
b
x
s
s
sn
,
where

2
2
ii
yy
s
n
and

2
1
i
x
x x
s
n
*Standard deviation is a measurement of variability from the theoretical population. Standard error is the estimate of the standard deviation. If the standard
deviation of the statistic is assumed to be known, then the standard deviation should be used instead of the standard error.
© 2025 College Board
 2AP Statistics
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End of Document
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FAQs

What are the key formulas for descriptive statistics in AP Statistics?
Descriptive statistics in AP Statistics include formulas for calculating the mean, median, mode, and standard deviation. The mean is calculated by summing all data points and dividing by the number of points. The standard deviation measures the dispersion of data points from the mean, providing insight into data variability. Understanding these formulas is crucial for analyzing data sets and interpreting statistical results.

How are probability distributions represented in AP Statistics?
Probability distributions in AP Statistics are represented through functions that describe the likelihood of different outcomes. For discrete random variables, the probability mass function (PMF) defines the probability of each possible value. For continuous random variables, the probability density function (PDF) is used. Key distributions covered include binomial and geometric distributions, each with specific formulas for calculating probabilities and expected values.

What is the significance of confidence intervals in statistical analysis?
Confidence intervals provide a range of values within which the true population parameter is likely to fall, based on sample data. They are crucial for estimating parameters such as means and proportions with a specified level of confidence, often set at 95% or 99%. Understanding how to calculate and interpret confidence intervals is essential for making informed decisions based on statistical data.

What topics are included in the sampling distributions section?
The sampling distributions section includes key concepts such as the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as sample size increases. It also covers the standard error of the mean and the standard error of proportions, which are vital for understanding the variability of sample statistics. These concepts are fundamental for conducting hypothesis tests and constructing confidence intervals.