Frequently Used Statistics Formulas and Tables PDF

Frequently Used Statistics Formulas and Tables

Probability of the complement of event. ( ) = 1 - ( ). Multiplication rule for *see table 7-2 (last page of formula sheet). Confidence Intervals. Level of ...

Statistics Formula Sheet and Tables 2020

AP Statistics 2020 Formulas and Tables Sheet. Page 4. Probability z. Table entry for z is the probability lying below z. Table A (Continued) z .00 .01 .02 .03.

Probability & Statistics Facts Formulae and Information

Jan 11 2023 mathcentre is a project offering students and staff free resources to support the transition from school mathematics to university.

BIOINFORMATICS MSc PROBABILITY AND STATISTICS

PROBABILITY AND STATISTICS FORMULA SHEET. SET THEORY DEFINITIONS AND RESULTS. Events E and F are mutually exclusive if E

ap-biology-equations-and-formulas-sheet.pdf

Apr 13 2019 AP® BIOLOGY EQUATIONS AND FORMULAS. Statistical Analysis and Probability. Mean. -. I n x= -I n i=I. Standard Error of the Mean. SE- =_!__. X.

Statistics Cheat Sheet

Read the table of t-distribution critical values for the p-value (probability that the sample mean was obtained by chance given μ0 is the population mean)

ap stat formula sheet

Tables for AP Statistics. Probability. N. Table entry for Z is the probability lying below Z. Table A Standard Normal Probabilities. Z .00 .01 .02 .03 .04 .05.

List MF19

List of formulae and statistical tables. Cambridge International AS & A Level FURTHER PROBABILITY & STATISTICS. Sampling and testing. Two-sample estimate of ...

Formula Sheet for Final Exam

= P(A) + P(B) − P(A and B). • Conditional probability: P(A

Important Concepts not on the AP Statistics Formula Sheet

Major Concepts in Probability. For the expected value (meanµX) and the. 2 or X. X σ σ of a probability distribution use the formula sheet. Binomial Probability.

Frequently Used Statistics Formulas and Tables

Math PRB nCr enter r. Note: textbooks and formula sheets interchange “r” and “x” for number of successes. Chapter 5. Discrete Probability Distributions:.

Statistics Formula Sheet and Tables 2020

Formulas and Tables for AP Statistics. I. Descriptive Statistics Probability and Distributions ... AP Statistics 2020 Formulas and Tables Sheet ...

Formula Sheet for Final Exam

Formula Sheet for Final Exam. Summary Statistics Conditional probability: P(A

Statistics Cheat Sheet

Read the table of t-distribution critical values for the p-value (probability that the sample mean was obtained by chance given ?0 is the population mean)

Statistics Cheat Sheet

Read the table of t-distribution critical values for the p-value (probability that the sample mean was obtained by chance given ?0 is the population mean)

Engineering Formula Sheet

Engineering Formula Sheet. Probability. Pk = n!(pk)(qn-k) k!(n-k)!. Binomial Probability (order doesn't matter). Pk = binomial probability of k successes in

ap-biology-equations-and-formulas-sheet.pdf

00762-113-CED-Biology_Appendix.indd 214. 4/13/19 6:27 PM. AP® BIOLOGY EQUATIONS AND FORMULAS. Statistical Analysis and Probability.

Important Concepts not on the AP Statistics Formula Sheet

Find the t-test statistic and p-value for the effect cry count has on IQ. of a probability distribution use the formula sheet. Binomial Probability.

TI 83/84 Calculator – The Basics of Statistical Functions

Ch Topic. Calculator. Formulas Tables

Probability Cheatsheet v2.0

Sep 4 2015 Uniform Order Statistics The jth order statistic of. i.i.d. U1

Statistics Formula Sheet and Tables 2020 - AP Central

Probability Distribution Mean Standard Deviation Discrete random variable X ; AP Statistics 2020 Formulas and Tables Sheet 14: 2)

Chance and Probability: Probability Formula Solved

i) The Law of Total Probability For disjoint events C 1;C 2;:::;C mthat partition P(A) = P(AjC 1)P(C 1) + P(AjC 2)P(C 2) + + P(AjC m)P(C m) This allows us to write a probability P(A) as a weighted sum of conditional probabil- ities Useful when the conditional probabilities are known or easy

Frequently Used Statistics Formulas and Tables

Standard deviation of a probability distribution: ? = ?[ x 2• P( x)]?µ2 Binomial Distributions =number of successes (or x) = probability of success = probability of failure =?1 p +q= 1 Binomial probability distribution (r )=nCr pr qn?r Mean: µ=np Standard deviation: ?= npq Permutation and Combination on TI 83/84

ENGINEERING PROBABILITY AND STATISTICS - University of Memphis

LAWS OF PROBABILITY Property 1 General Character of Probability The probability P(E) of an event E is a real number in the range of 0 to 1 The probability of an impossible event is 0 and that of an event certain to occur is 1 Property 2 Law of Total Probability P(A + B) = P(A) + P(B) – P(A B) where

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Conditional ProbabilityisProbabilityP(AjB) is a probabilityfunction for any xedB Any theorem that holds for probability alsoholds for conditional probability Probability of an Intersection or Union Intersections viaConditioning P(A; B) =P(A)P(BjA)P(A; B; C) =P(A)P(BjA)P(CjA; B) Unions via Inclusion-Exclusion

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Set books The notes cover only material in the Probability I course The text-books listed below will be useful for other courses on probability and statistics You need at most one of the three textbooks listed below but you will need the statistical tables • Probability and Statistics for Engineering and the Sciences by Jay L De-

What is the equation of probability?

The equation of probability is as follows: P (E) = Number of desirable events ÷ Total number of outcomes Using this formula let us calculate the probability of the above example. Here the desirable event is that your dice lands on a six, so there is only one desirable event.

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How do you calculate the probability of an event?

Probability Calculations Often, the calculation of the probability of an event involves combinatorics. We must count the number of points in the event as well as the number of points in the entire probability space. When points are equally likely, the ratio of these two counts is the probability of the event.

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Probability and statistics solved problems pdf is prepared by expert teachers. These probability aptitude questions based on recent updates and the exact syllabus of the competitive exam. So candidates can follow these problem-solving examples with solutions to understand the concepts and questions format as per the latest exam syllabus pattern.

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

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:

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

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

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

for ( 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 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 nn dfn n

Matched pairs (dependent samples)

Confidence Interval

where with d.f. = 1

Hypothesis Test

with . . 1 d d d d dE dE sEtnn d tdf ns n

Two Sample Variances

22
22
12 2 22
111
222
2 2 22
1 122
2 12

Confidence Interval for and

Hypothesis Test Statistic: where

numerator . . 1 and denominator . . 1 rightleft ss FF ss s F sss df ndf n 5

Chapter 10 Regression and Correlation

2 22 2

Linear Correlation Coefficient (r)

OR () where z score for x and z score for y1 explained variation

Coefficient of Determination: total v

xy xy n xy x yr nx x ny y zz rz zn r 2 2 01 2 0 /222 2 ariation ()Standard Error of Estimate: s2 or s 2

Prediction Interval:

1where 1( )()

Sample test statistic for

with 1 2 e e e yy n y b y b xy n yE yyE nx x

Et snnx x

r rt r n .. 2df n Least-Squares Line (Regression Line or Line of Best Fit) 0101
11 22
2 00122
note that is the y-intercept and is the slope where or ( )( ) where or ( )( ) y x y b bxbb s n xy x ybbrsnx x and y x x xybb y bxnx x 0 0 00quotesdbs_dbs11.pdfusesText_17

[PDF] Frequently Used Statistics Formulas and Tables

What is the equation of probability?

What are worksheets in probability?

How do you calculate the probability of an event?

What is probability and statistics solved problems PDF?

Frequently Used Statistics Formulas and Tables

Chapter 2

Class Midpoint = 2

Chapter 3

Sample mean:

Population mean:

Weighted mean:

Mean for frequency table:

Midrange2x

Range = Highest value - Lowest value

Sample standard deviation: 1

Population standard deviation:

Sample variance:

Population variance: xx

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

Sample z-score:

Population z-score: xx

Interquartile Range: (IQR)

Modified Box Plot Outliers

Chapter 4

Multiplication rule for independent even

General multiplication rules

P not A P A

P A and B P A P B

P A and B P A P B given A

General addition rule

Permutation and Combination on TI 83/84

Note: textbooks and formula

Chapter 5

Discrete Probability Distributions:

Mean of a discrete probability distribution:

Binomial Distributions

1 = 1

Binomial probability distribution

Standard deviation:

Pr Cpq

Poisson Distributions

Poisson probability distribution

2.71828

Chapter 6

Normal Distributions

Raw score:

Standard score: xz

Mean of distribution:

Standard deviation of distribtuion:

Standard score for :

Chapter

One Sample

Confidence Interval

Chapter 7

Confidence Interval: Point estimate ± error

Point esti

Upper limit + Lower limit

Error = Upper limit - Lower limit

0.25 without preliminary estimate for z

Sample Size for Estimating

Confidence Intervals

Level of Confidence z-value

70% 1.04

75% 1.15

80% 1.28

85% 1.44

90% 1.645

95% 1.96

98% 2.33

for ( 5 and 5): /