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

[PDF] Frequently Used Statistics Formulas and Tables

Sample Size for Estimating variance or standard deviation: *see table 7-2 (last page of formula sheet) Confidence Intervals Level of Confidence z-value ( /2 z α )

[PDF] Descriptive Statistics – Summary Tables

The values of a Group Variable are used to define the rows, sub rows, and columns of the summary table Up to two Group Variables may be used per table Group 

[PDF] 4 Introduction to Statistics Descriptive Statistics - PDF4PRO

The confidence interval formula can be helpful For example, for Normal data, confidence interval for is ̅ √ Suppose we want to estimate to within , where ( 

[PDF] Basic Descriptive Statistics 2016docx - Department of Statistics

All rights reserved Basic Descriptive Statistics in Excel 2016 Select the Height variable and copy it into a new sheet 2 the appropriate formulas for each of the remaining cells to complete the table Formula Reference: Descriptive Statistic

[PDF] Statistics Formula Sheet and Tables 2020 - AP Central

Formulas and Tables for AP Statistics I Descriptive Statistics 1 i i x x x n n ∑ = ∑ = expected χ − = ∑ 2 AP Statistics 2020 Formulas and Tables Sheet 

[PDF] Introduction to descriptive statistics - The University of Sydney

Introduction to Descriptive Statistics Jackie Nicholas Deviation of a Population The formula for the mean (average) of N observations is given by: μ = 1 N N

[PDF] Descriptive Statistics - NCSS

of descriptive statistics, errors in interpretations are very likely Missing Data Several of the formulas involve both raw and central moments The raw moments  

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examples of descriptive statistics and they help us to explain the data more accurately and in greater detail In this equation we compute the difference between each raw value and the mean (X org/ pdf /8226 pdf References 131 © Jones 

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Chapter 3 Descriptive Statistics 47 3 DESCRIPTIVE are given by A1 and A2, then the formula for the corresponding radii is given by A1 A2 = π r1 2 π r2

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the data, something that descriptive statistics does not do Other distinctions The variance σ2 of a whole population is given by the equation σ2 = Σ(x − µ)2 n

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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 t 12 22
12 12 12 with . . smaller of 1 and 1 ss nnquotesdbs_dbs17.pdfusesText_23