Elementary Statistics Formulas

ELEMENTARY STATISTICS, 5/E

Neil A. Weiss

FORMULAS

NOTATION The following notation is used on this card:

n

sample size

σ

population stdev

x

sample mean

d

sample stdev

p

ˆ

Probability and Random Variables

• Probability for equally likely outcomes:

paired difference

s

CHAPTER 5

sample proportion

j th quartile

p

population proportion

N

population size

O

observed frequency

µ

population mean

E

expected frequency

Qj

where f denotes the number of ways event E can occur and

N denotes the total number of outcomes possible.

• Special addition rule:

P (A or B or C or · · · )

CHAPTER 3

Descriptive Measures

• Sample mean: x

• Range: Range

• Complementation rule: P (E)

or

x 2 − ( x)2 /n

n−1

s

Q3 − Q1

Q1 − 1.5 · IQR,

Upper limit

Q3 + 1.5 · IQR

x

N

σ

(x − µ)2 P (X

(x −

N

x2

σ

N

− µ2

• Sxx , Sxy , and Syy :

Sxy

(x − x)(y − y)

Syy

(y − y)2

• Regression equation: y

ˆ

b1

Sxy

Sxx

and

x 2 − ( x)2 /n

1

( y − b1 x)

n

(y − y)2

• Regression sum of squares: SSR

• Error sum of squares: SSE

• Regression identity: SST

y − b1 x

Syy

(y − y)2

ˆ

(y − y)2

ˆ

2

Sxy /Sxx

2

Syy − Sxy /Sxx

SSR + SSE

• Coefficient of determination: r 2

r

sx sy

np

• Standard deviation of a binomial random variable: σ

SSR

SST

µ

√

σ/ n

• Standard deviation of the variable x : σx

Confidence Intervals for One Population Mean

• Standardized version of the variable x :

z

x−µ

√

σ/ n

• z-interval for µ (σ known, normal population or large sample):

σ

x ± zα/2 · √

n

σ

zα/2 · √

n

• Sample size for estimating µ:

n

or

r

Sxy

Sxx Syy

np(1 − p)

The Sampling Distribution of the Sample Mean

• Margin of error for the estimate of µ: E

• Linear correlation coefficient:

(x − x)(y − y)

nx

p (1 − p)n−x ,

x

x)

where n denotes the number of trials and p...