[PDF] [PDF] Frequently Used Statistics Formulas and Tables

[PDF] Frequently Used Statistics Formulas and Tables

Frequently Used Statistics Formulas and Tables Chapter 2 highest value Class Midpoint = 2 Chapter 3 sample size Chapter 12 One Way ANOVA 2 2 2 2

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Frequently Used Statistics Formulas and Tables

Chapter 2

highest value - lowest valueClass Width = (increase to next integer)number classes upper limit + lower limit

Class Midpoint = 2

Chapter 3

sample size population size frequencyn N f sum w weight

Sample mean:

Population mean:

Weighted mean:

Mean for frequency table:

highest value + lowest value

Midrange2x

xn x N wxxw fx xf 2 2 2 2

Range = Highest value - Lowest value

Sample standard deviation: 1

Population standard deviation:

Sample variance:

Population variance: xx

s n x N s

Chapter 3

Limits for Unusual Data

Below : - 2

Above: 2

Empirical Rule

About 68%: - to

About 95%: -2 to 2

About 99.7%: -3 to 3

22Sample coefficient of variation: 100%

Population coefficient of variation: 100%

Sample standard deviation for frequency

table: ( 1)s CVx CV n fx fx snn

Sample z-score:

Population z-score: xx

zs x z 31
1 3

Interquartile Range: (IQR)

Modified Box Plot Outliers

lower limit: Q - 1.5 (IQR) upper limit: Q + 1.5 (IQR)QQ 2

Chapter 4

Probability of the complement of event ( ) = 1 - ( )

Multiplication rule for independent even

ts

General multiplication rules

( ) ( ) ( , ) A

P not A P A

P A and B P A P B

P A and B P A P B given A

Addition rule for mutually exclusive events ( ) ( ) + ( )

General addition rule

( ) ( ) + ( ) ( )P A and B P A P A given BPAorB PA PBP A or B P A P B P A and B !Permutation rule: ( )! nr nPnr !Combination rule: !( )! nr nCrnr

Permutation and Combination on TI 83/84

n Math PRB nPr enter r n Math PRB nCr enter r

Note: textbooks and formula

sheets interchange "r" and "x" for number of successes

Chapter 5

Discrete Probability Distributions:

22

Mean of a discrete probability distribution:

Standard deviation of a probability distribution: [ ( )]x Px x Px

Binomial Distributions

number of successes (or x) probability of success = probability of failure

1 = 1

Binomial probability distribution

Mean:

Standard deviation:

r nr nr r p q q p pq

Pr Cpq

np npq

Poisson Distributions

2 number of successes (or ) = mean number of successes (over a given interval)

Poisson probability distribution

2.71828

(over some interval) r rx e Prr e mean 3

Chapter 6

Normal Distributions

Raw score:

Standard score: xz

x z

Mean of distribution:

Standard deviation of distribtuion:

(standard error)

Standard score for :

x x x x n x xzn

Chapter

7

One Sample

Confidence Interval

/2 for proportions ( ): ( 5 and 5) (1 ) where p np nq pE p pE ppEzn rpn /2 /2 for means ( ) when is known: where for means ( ) when is unknown: where with . . 1xE xE Ezn xE xE sEtn df n

Chapter 7

Confidence Interval: Point estimate ± error

Point esti

mate =

Upper limit + Lower limit

2

Error = Upper limit - Lower limit

2 2 /2 2 /2 2 /2 means: proportions: with preliminary estimate for

0.25 without preliminary estimate for z

nE z n pqpE z npE

Sample Size for Estimating

v ariance or standard deviation: see table 7-2 (last page of formula sheet)

Confidence Intervals

Level of Confidence z-value

/2 z

70% 1.04

75% 1.15

80% 1.28

85% 1.44

90% 1.645

95% 1.96

98% 2.33

99% 2.58

22
22
22
( 1) ( 1)for variance ( ): < with . . 1 RL ns ns df n 4

Chapter

8 One

Sample

Hypothesis

Testing

2 22
2

ˆfor ( 5 and 5): /

where 1 ; / for ( known): for ( unknown): with . . 1 ( 1) for : with . . 1pp p np nq zpq n q pp rn x zn xtdf nsn ns df n

Chapter 9

Two Sample Confidence Intervals

and Tests of Hypotheses 12 ppDifference of Proportions ( )

12 12 12

11 22 /2 12

1 1 1 2 2 2 1 12 2

12 12 12

Confidence Interval:

where / ; / and 1 ; 1

Hypothesis Test:

where the poolpp E pp pp E pq pq Eznn p rnp r n q pq p pp pp zpq pq nn 12 12

1 112 22

ed proportion is and 1 / ; /p rr p qpnn p rnp rn

Chapter 9

2 1

Difference of means

ȝ ȝ ples)

12

12 1 2 12

22
12 /2 12 12

12 1 2

22
12 12

Confidence Interval when and are known

where

Hypothesis Test when and are known

( )( ) xx E xx E Ez nn xx z nn 12

12 1 2 12

22
12 /2 12 12 12 12

Confidence Interval when and are unkno

wn with . . = smaller of 1 and 1

Hypothesis Test when and are unknown

xx E xx E ss Etnn dfn n xx tquotesdbs_dbs17.pdfusesText_23