Acorn Book (and where they are in IPS) ( (I) Descriptive ...

n(The sample mean of a data set.)

AP Statistics: Formulas from the Acorn Book and what they mean(and where they are in IPS)

( (I) Descriptive Statistics

Ix;• X=

• sx = IlL (x , - x) 2 (The sample standard deviation.s1n -1

• s =p

(nl-1)s~ + (n2-1)s~(Pooled estimator oj G, the population

(nj-1) + (n2-1)standard deviation for two-sample tprocedures. Assumes populations haveequal variances. ., Generalized inANOVA.)

• y = bo + bjx (The least squares regression line in which bo estimatesf30 and b J estimates f3 J 1 .

•L (Xi - x)(y; - y)

L (X; - X)2(The slope of the least squares regression

• b =y--bxo J

line.) _

(The y-intercept of the least squares regression line.) .~.~,

• (The correlation coefficients:

• b J = r:r. (Linear relationship between the slope of the regression linesx

and the correlation coefficient.)

1

Source: Duane Hinders\ r:: \

! .

•

L (Yi - y)2n - 2

Sb =, JUx, - i)'

(II) Probability

(Standard error of the slope of the regression

line.)

• peA u B) = prAY + PCB) - peA n B) (Addition Rule for Unions ofTwo Events) .. ..

• peA I B) = peA n B) (Conditional probability of A given B.)PCB)

• (Mean (expected value) of a discrete random

variable X.). -

• (Variance of a discrete random

variable X.):If X has a binomial distribution with parameters nand p , then:

• P(X = k) = (;) pk(J ~ »:: (Probability of getting exactly k successes

in n observations of an event that occurswith probability, ) ~. ,

• J..ix = np (Mean of a binomially distributed random variable.) .;

(Standard deviation of a binomially distributedrandom variable. )~_ -

(Mean of a sampleproportion.) ..

• a =A~np(l - p) .

•

• (Standard deviation of a sample proportion.) ..

2Source: Duane Hinders

i ~ C.

('\ ...•......

If X has a normal distribution with mean J.l and standard deviation a, then:

(Mean of a sampling distribution of sample means.) _, '•l, '

•a

a--x - rn (Standard deviation of a sampling distribution of sample means

-- standard error of the mean. }

(III) Inferential Statistics

Single Sam pie

mean a d.f. = n-l)(x) in

proportion ~p(1 n-P) :-!

(p)

········s· ···························S.. '.r~.·d··n t·· .......... ~.~I~tl~ ~Q~{ ~y.~~'QQ .

T S I

<wo amrne

Statistic Standard Deviation

difference of means ~ 0;(unequal variances) ~ n1 + nz

- ".=-;, ,(x 1- x z) .'

.. ' ,

(d.f. = min{nJ-I,n2-1})

difference of means.

a~ 1 + 1/

(equal variances) (x]- x) (d.f. = n] + n2 -2)n 1 nz

difference of proportions (jJ - Pz) Pj(1 - p) Pz(1 - pz) ,(unequal variances) .1\ +

n1 nz

difference of proportions J0T(equal variances) (PI -pz) ~p(1 - p) - + - ,0'

n 1 nz

. .. (observed - expectedt'Chi-square test statisnc = L~------!------::-expected

, (For a two-way table, d.f. = (r - l)(c - 1); for Goodness-of-Fit. d.f = n - 1)

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Source: Duane HindersIC:-,