Formulas for AP Statistics

[Pages:2]Formulas for AP Statistics

I. Descriptive Statistics

x

1 n

?

xi

? xi

n

y^ a bx

? r

1 n 1

? ? ?

xi sx

x

? ? ?

? ???

yi sy

y

? ???

sx

n

1

1

?

xi

x

2

y a bx

b

r

sy s x

?xi x 2

n 1

II. Probability and Distributions

PAB PA PBPAB

P(A | B)

P(A B) P(B)

Probability Distribution Discrete random variable, X

If X has a binomial distribution with

parameters n and p, then:

PX

x

? ? ?

n x

? ? ?

p

x

1

p

n

x

where x 0, 1, 2, 3, ! , n

If X has a geometric distribution with parameter p , then:

P X x  1 p x1 p

where x 1, 2, 3, !

Mean

?X = E( X ) = ?xi P (xi )

PX np

P X

1 p

Standard Deviation

? X =

(xi - ?X )2 P ( xi )

V X np1 p

VX

1 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 =

(observed - expected)2

expected

AP StatisticsCourse and Exam Description

AppendixV.1|254

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? 2019 College Board

III. Sampling Distributions and Inferential Statistics (continued)

Sampling distributions for proportions:

Random Variable

For one population:

p^

For two populations:

p^1 - p^2

Parameters of Sampling Distribution

Pp^ p

V p^

p1 p

n

P p p p^1 p^2

1

2

V p^1 p^2

p1 1 p1  p2 1 p2

n1

n2

Sampling distributions for means:

Standard Error* of Sample Statistic

s p^

p^ 1 p^

n

s p^1 p^2

p^1 1 p^1  p^2 1 p^2

n1

n2

When p1 p2 is assumed:

( ) s = p^1-p^2

p^c

1 - p^c

? ? ?

1 n1

+

1 n2

? ? ?

where p^c

X1 X2 n1 n2

Random Variable

For one population:

X

For two populations:

X1 X2

Parameters of Sampling Distribution

PX P

V X

V n

PX1 X2 P1 P2

V X1 X2

V

2 1

V

2 2

n1 n2

Sampling distributions for simple linear regression:

Standard Error* of Sample Statistic

sX

s n

sX1 X2

s12 s22 n1 n2

Random Variable

For slope:

b

Parameters of Sampling Distribution

Pb E

Vb

V, Vx n

where V x

? xi x 2

n

Standard Error* of Sample Statistic

sb

s, sx n 1

where s

? yi yi 2

n2

and sx

?xi x 2

n 1

*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.

AP StatisticsCourse and Exam Description

AppendixV.1|255

Return to Table of Contents

? 2019 College Board

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