Statistics Formula Sheet and Tables 2020

Statistics Formula Sheet and Tables 2020

The Statistics Formula Sheet and Tables 2020 provides essential formulas and statistical tables for students and professionals in statistics. It covers key topics such as descriptive statistics, probability distributions, sampling distributions, and inferential statistics. This resource is particularly useful for AP Statistics students preparing for exams, offering a concise reference for calculations and statistical concepts. The document includes standardized test statistics, confidence intervals, and critical values for various distributions, making it a comprehensive tool for understanding statistical methodologies. Ideal for quick reference during study sessions or exam preparations.

Key Points

  • Includes formulas for descriptive statistics, probability distributions, and inferential statistics.
  • Provides critical values for z, t, and chi-square distributions essential for hypothesis testing.
  • Covers sampling distributions for both proportions and means, aiding in statistical analysis.
  • Features a probability table for standard normal distribution, useful for calculating probabilities.
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Formulas and Tables for AP Statistics
I. Descriptive Statistics
1
i
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
r
n 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
=
X
np
(
1 p
)
If 𝑋𝑋 has a geometric distribution
with parameter p, then:
PX
(
= x
)
=
(
1 p
)
x1
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 Statistics2020 Formulas and Tables Sheet
*S
tandard 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.
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
(
1
)
p
σ
p
ˆ
=
n
µ
p
ˆ
= p
p
p
ˆ
(
1
)
s
p
ˆ
=
n
p
ˆ
For two
populations:
p
1
p
ˆˆ
2
µ
= p
pp
ˆˆ
1
12
p
p
(
1
σ
1
pp
12
) ( )
= +
pp
ˆˆ
12
n
1
p1
2
2
n
2
p
ˆ
s
1
1pp
ˆˆ
12
= +
pp
ˆˆ
12
n
1
(
1
) (
p
ˆ
2
)
n
2
When
p=
1
is assumed:
p
2
s=pp
(
1
ˆˆ
1
pp
ˆˆ
c c
)
12
nn
1
1
+
2
XX
+
p
ˆ
=
1
c
nn
+
where
2
12
Sampling distributions for means:
Random
Variable
Parameters of Sampling Distribution
Standard Error
*
of Sample Statistic
For one
population:
X
µ
=
X
σ
σ
=
X
n
µ
s
s =
X
n
For two
populations:
XX
12
µ
=
µ
XX
1
12
µ
2
σσ
22
σ
=
12
+
XX
12
n
12
n
ss
2
s =
1
+
XX
12
nn
1
2
2
2
Sampling distributions for simple linear regression:
Random
Variable
Parameters of Sampling Distribution
Standard Error
*
of Sample Statistic
For slope:
b
σ
σ
=
b
,
σ
x
n
( )
2
∑−xx
σ
=
i
x
n
where
s
s =
b
,
sn 1
x
(
ˆ
)
2
∑−yy
s =
ii
n
2
( )
2
∑−xx
s =
i
x
n 1
and
where
AP Statistics2020 Formulas and Tables Sheet
b
=
µ
β
Probability
z
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AP Statistics2020 Formulas and Tables Sheet
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FAQs of Statistics Formula Sheet and Tables 2020

What key formulas are included in the Statistics Formula Sheet?
The Statistics Formula Sheet includes essential formulas for descriptive statistics, such as mean, median, and standard deviation. It also covers probability distributions, including binomial and geometric distributions, with their respective means and standard deviations. Additionally, it provides formulas for sampling distributions, including those for proportions and means, which are crucial for inferential statistics. This comprehensive collection serves as a quick reference for students and professionals alike.
How does the document assist with AP Statistics exam preparation?
The Statistics Formula Sheet is designed to aid AP Statistics students in their exam preparation by consolidating key formulas and statistical concepts in one place. It includes standardized test statistics and critical values necessary for hypothesis testing, which are commonly featured in AP exam questions. By having quick access to these formulas and tables, students can efficiently solve problems and understand the underlying statistical principles. This resource is particularly valuable during study sessions leading up to the exam.
What types of distributions are covered in the Statistics Formula Sheet?
The Statistics Formula Sheet covers several types of distributions, including normal, binomial, and geometric distributions. Each distribution is accompanied by its respective formulas for calculating probabilities, means, and standard deviations. Additionally, the document provides critical values for t-distributions and chi-square distributions, which are essential for conducting hypothesis tests. This comprehensive overview of distributions helps users understand and apply statistical methods effectively.
What is the significance of the probability table included in the document?
The probability table included in the Statistics Formula Sheet provides values for the standard normal distribution, which is crucial for calculating probabilities associated with z-scores. This table allows users to quickly find the probability that a standard normal random variable is less than a given z-value. Understanding how to use this table is fundamental for conducting hypothesis tests and making inferences based on sample data. It enhances the overall utility of the document for students and professionals in statistics.

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