AP Statistics Formula Tables for Exam Preparation

AP Statistics Formula Tables for Exam Preparation

AP Statistics formula tables provide essential statistical formulas and concepts for students preparing for the AP exam. These tables include key formulas for descriptive statistics, probability distributions, sampling distributions, and inferential statistics. Students can find detailed explanations of standard deviations, confidence intervals, and chi-square statistics. This resource is ideal for AP Statistics students looking to reinforce their understanding of statistical principles and improve their exam performance.

Key Points

  • Includes comprehensive formulas for descriptive statistics and probability distributions essential for AP Statistics.
  • Covers sampling distributions for means and proportions, providing clarity on standard errors and confidence intervals.
  • Details the chi-square statistic and its application in hypothesis testing for categorical data.
  • Offers a standard normal probabilities table to assist with z-scores and probability calculations.
, ,
  • newtopiccyclegrowin
352
/ 10
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
Tables for AP Statistics
Table entry for z is the probability lying below z.
Table A Standard Normal Probabilities
z
.00 .01 .02 .03 .04 .05 .06 .07 .08 .09
−3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002
−3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003
−3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005
−3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007
−3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010
−2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014
−2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019
−2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026
−2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036
−2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048
−2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064
−2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084
−2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110
−2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143
−2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183
−1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233
−1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294
−1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367
−1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455
−1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559
continued on next page
© 2025 College Board
 3AP Statistics
/ 10
End of Document
352
You May Also Like

FAQs of AP Statistics Formula Tables for Exam Preparation

What key formulas are included in the AP Statistics formula tables?
The AP Statistics formula tables include essential formulas for descriptive statistics, such as mean, median, mode, and standard deviation. Additionally, it covers probability distributions, including binomial and geometric distributions, along with their respective means and standard deviations. The tables also provide formulas for sampling distributions, confidence intervals, and hypothesis testing, making it a comprehensive resource for students preparing for the AP exam.
How do the formula tables assist in understanding sampling distributions?
The formula tables provide clear definitions and formulas for sampling distributions of both means and proportions. For means, it outlines the relationship between the population standard deviation and sample size, helping students calculate the standard error. For proportions, it explains how to compute the standard error of the sample proportion, which is crucial for constructing confidence intervals and conducting hypothesis tests.
What is the significance of the chi-square statistic in AP Statistics?
The chi-square statistic is a vital tool in AP Statistics for testing relationships between categorical variables. The formula tables detail how to calculate the chi-square statistic using observed and expected frequencies, which is essential for conducting chi-square tests of independence and goodness-of-fit. Understanding this statistic allows students to analyze data effectively and draw conclusions about population characteristics.
How can students use the standard normal probabilities table effectively?
The standard normal probabilities table is a crucial resource for students working with z-scores in AP Statistics. It provides the probability of a value falling below a given z-score, which is essential for understanding the normal distribution. Students can use this table to find critical values for hypothesis testing and confidence intervals, enhancing their ability to interpret statistical results.

Related of AP Statistics Formula Tables for Exam Preparation