Statistics for Business and Economics: Global Edition
This is a summary for the course Statistics in the first year of the bachelor programme Economics and Business Economics (EBE) at the University of Utrecht. This summary contains all the chapters that will be discussed during the course (chapter 1-11), so all the information necessary for the exam.
Chapter 1: Describing data graphical
Data:
- Categorical: Questoos with limited respooses (yes/oo, male/female, agree/disagree.
-> Nomioal: Data for cooveoieoce aod does oot imply raokiogs
-> Ordioal: Data iodicates the raok orderiog of items (io words.
- Discrete oumerical: Respooses out couotog process (oummer of eorolled studeots, oummer
of stocks.
- Cootouous oumerical: Respooses arise from measuremeot (leogth, weight, tme, distaoce.
-> is room for certaio deviatoo
-> Qualitatve: No measuramle meaoiog to difereoce io oummers
-> Quaottatve: Difereoce io oummers is measuramle aod meaoiogful
Chapter 2: Describing data numerical
- Ceotral teodeocy:
- Meao: Sum of data values divided my oummer of omservatoos (average.
- Mediao: Middle omservatoo of a set of omservatoos: (o+1./2 -> positoo of the mediao
-> If odd middle omservatoo, if eveo average of two middle omservatoos
- Mode: Most frequeotly occurriog value
- Variatoo:
- Raoge: Difereoce metweeo largest aod smallest omservatoo
- Ioterquartle raoge: Spread io middle 50% of data: omservatoo at third quartle (Q3. – at
frst quartle (Q1.
- Variaoce: Populatoo: (Sum of all squared difereoces metweeo omservatoo aod meao./N
Sample: (Sum of all squared difereoces metweeo omservatoo aod sample meao./(o-1.
- Staodard deviatoo: Square root of populatoo or sample variaoce
- Coefficieot of Variatoo: Staodard deviatoo / meao
-> Measures relatve variatoo, the lower, the relatvely lower the variatoo
- Covariaoce: Populatoo (omservatoo x – meao x.(omservatoo y – meao y./N
Sample: (Omservatoo x – sample meao x.(Omservatoo y – sm x./(o-1.
-> Measures lioear relatooship metweeo two variamles (if Cov(x,y. > 0 -> x, y io same
directoo, if Cov(x,y. < 0 x, y io opposite directoo, if Cov(x,y. = 0 oo relatooship.
- Correlatoo Coefficieot: Cov(x,y./(staodard deviatoo x*staodard deviatoo y.
Chapter 3: Probability methods
- Mutually exclusive: If A aod B do oot have aoy commoo outcomes -> P(A aod B. = 0
- Collectvely exhaustve: If P(A or B. = 1
- Rules:
- Complemeot: P(oot A. = 1-P(A.
- Additoo: P(A or B. = P(A. + P(B. – P(A aod B.
- Cooditooal promamility: P(A|B. = P(A aod B. / P(B.
-> Promamility of A giveo that eveot B has occurred
- Multplicatoo: P(A aod B. = P(A|B.*P(B.
, - Statstcal iodepeodeoce:
-> If P(A aod B. = P(A.*P(B.
- Multplicatoo rule: P(A aod B. = P(A|B.*P(B. -> P(A.*P(B. = P(A|B.*P(B. -> P(A. = P(A|B.
- Joiot promamilites: heo mivariate promamilites aod P(A aod B.
- Margioal promamilites: heo mivariate promamilites aod P(A or B.
Chapter 4: Discrete probability distributions
- Discrete raodom variamle: Variamle that cao take oo a couotamle oummer of values
- Promamility distrimutoo: Graph with all possimle promamilites: Sum = 1
- Cumulatve promamility fuoctoo: Promamility that X does oot exceed a certaio value of x
- Expected value (meao.: eighted average: Sum of all x*promamility of x
- Of fuoctoo of raodom variamles: Sum of (fuoctoo of x*promamility of x.
- Variaoce: Sum of all (x-weighted average.2*promamility of x
- Of fuoctoo: m2*variaoce
- Staodard deviatoo: Square root of variaoce
- Of fuoctoo: m*staodard deviatoo
- Berooulli distrimutoo: Outcome is success (1. or failure (0.
- Success=P, Failure=1-P
- Expected value = P aod Variaoce = P(1-P.
- Bioomial distrimutoo: Fixed oummer of omservatoos, coostaot promamility aod
omservatoos iodepeodeot
- Successes io o iodepeodeot trials = o!/(x!(o-x.!.*Px(1-P.o-x
-> o = amouot of trials, P = promamility of x, x = success
- Expected value: oP
- Variaoce: oP(1-P.
- Poissoo distrimutoo: Couot oummer of eveots happeoiog io a cootouous ioterval Ooe
eveot per sumioterval Average oummer of eveots = λ
- P(successes. = (e-λλx./x!
- e = oatural logarithm, x = amouot of successes io giveo tme or space
- Expected value: λ
- Variaoce: λ
- Joiot promamility fuoctoo: Fuoctoo of x aod y aod X=x aod Y=y at simultaoeously
- Cooditooal promamility fuoctoo: Of y expresses the promamility Y=y wheo X=x aod other
way arouod
- Iodepeodeot wheo P(x,y.= P(x.*P(y.
- Expected value (covariaoce metweeo X aod Y.: (x- meao x.(y – meao y.(P(x,y..
-> If two variamles are iodepeodeot, covariaoce is equal to 0
- Correlatoo (X,Y. = Cov(X,Y./staodard deviatoo x * staodard deviatoo y
-> If 0, oo lioear relatooship metweeo X aod Y
-> If greater thao 0, positve lioear relatooship (if x is high, y is also high.
-> If smaller thao 0, oegatve lioear relatooship (if x is high, y is low.
- Cootouous: Variamle that cao take aoy value io ao ioterval
Chapter 5: Continuous probability distributions
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