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AP Stat

The document provides formulas for AP Statistics, covering descriptive statistics, probability and distributions, and inferential statistics. Key formulas include those for mean, standard deviation, and probability distributions for binomial and geometric variables. It also outlines concepts like standardized test statistics and confidence intervals.

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Evelyn Kim
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47 views1 page

AP Stat

The document provides formulas for AP Statistics, covering descriptive statistics, probability and distributions, and inferential statistics. Key formulas include those for mean, standard deviation, and probability distributions for binomial and geometric variables. It also outlines concepts like standardized test statistics and confidence intervals.

Uploaded by

Evelyn Kim
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Formulas for AP Statistics

I. Descriptive Statistics

1 ∑ xi 1 ∑ ( xi − x )2
x = ∑ xi = sx = ∑ ( xi − x )2 =
n n n −1 n −1

ŷ = a + bx y = a + bx

x − x   yi − y  sy
∑  i
1
r = b=r
n − 1  s x  s y  sx

II. Probability and Distributions


P ( A ∩ B)
P ( A ∪ B ) = P ( A) + P ( B ) − P ( A ∩ B ) P ( A | B) =
P ( B)

Probability Distribution Mean Standard Deviation

µ X = E ( X ) = ∑ xi P ( xi )
σ X = ∑ ( xi − µ X ) P ( xi )
2
Discrete random variable, X

If 𝑋𝑋 has a binomial distribution


with parameters n and p, then:
µ X = np σ X = np (1 − p )
n
P ( X = x ) =   p x (1 − p )n − x
 x
where x = 0, 1, 2, 3,  , n

If 𝑋𝑋 has a geometric distribution


1 1− p
with parameter p, then: µX = σX =
p p
P ( X = x ) = (1 − p ) x −1 p
where x = 1, 2, 3, 

III. Sampling Distributions and Inferential Statistics

statistic − parameter
Standardized test statistic:
standard error of the statistic

Confidence interval: statistic ± ( critical value )( standard error of statistic )

( observed − expected )2
Chi-square statistic: χ 2 = ∑ expected

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