Formula Sheet

FORMULA SHEET (page 1 of 3)

x = (xi)/n

Q1 Position = (n+3)/4

St.Dev. = Var

s2 = 1/(n-1)*[x2i - 1/n*(xi)2]

CV = ( s /x )*100

Q2 Position = (n+1)/2

Q3 Position = (3n+1)/4

Range = Max - Min

IQR = Q3 - Q1

Chebyshev's Rule: at least [100*(1-1/z2)]% where z = the number of st. dev.

Cov(X,Y) = sxy = 1/(n-1)*[xiyi - 1/n*(xi)*(yi)]

r = sxy/[sx*sy]

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P(A) = 1 - P(Ac)

P(A or B) = P(A) + P(B) - P(A and B)

P(A and B) = P(B|A)*P(A)

P(B|A) = P(A and B)/P(A)

Two events are mutually exclusive if P(A and B) = 0

Two events are independent if P(B|A) = P(B)

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E(X) = {xi*P(X=xi)}

Var(X) = [{x2i *P(X=xi)}] - [E(X)]2

n! = n*(n-1) *(n-2)*....*1

nCx

Binomial Distribution:

nCx *

= n!/[x!*(n-x)!]

px * (1-p)(n-x)

E(X)=n*p

Var(X)=n*p*(1-p)

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Normal Distribution:

E(X)=

Var(X)=2

Standard Normal Distribution:

E(Z)=0

Var(Z)=1

Z=(x-)/

Sampling Distribution of x:

E(x )=

Var(x )=2/n

Z=(x- )/(/n)

Sampling Distribution of p:

E(p )=p

Var(p )=p(1-p)/n

where p = x/n

Z=(p-p )/[p(1-p)/n]

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FORMULA SHEET (page 2 of 3)

Inference on , Known 

Zstat = (x - 0 ) / (/n )

C.I.: x  Z/2 (/n )

Inference on , Unknown 

tstat = (x - 0 ) / ( s/n )

C.I.: x  t/2,n-1 ( s/n )

Inference on p, Large Sample

Zstat = (p - p0 ) / [ p0(1-p0)/n ]

C.I.: p  Z/2 [ p(1-p)/n ]

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Inference on 1 - 2, Known s, Indep.Samples

Zstat = [(x1 - x2 ) - (1 - 2 )0] / [( 21/n1) + ( 22/n2)]

C.I.: (x1 - x2 )  Z/2[(...