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ECON1310: Quantitative Economic & Business Analysis A The University of Queensland 1 Descriptive Statistics 1 Population: Collection of everything in the universe with regards to the variable Parameter: A characteristic of the population Sample: Small group of things taken from the population Statistic: A characteristic of the sample Variable: Is a characteristic that we get data on Types of Sampling:

• Simple random sampling • Stratified random sampling • Systematic sampling • Cluster sampling • Convenience sampling • Judgement Sampling

2 Descriptive Statistics 2 Variability: Range= Maximum – minimum

Population Variance = !! = ! (!!!!)!!!! !!

!

Sample Variance = !! = ! (!!!!)!!!! !!

!

Population Standard deviation = ! = ! !! Sample standard deviation = s = !!

Sample co-efficient of variation (measures relative variability) = !"! = ! !! Measures of Association

Population Co-variance: !!" = !(!!!!!)(!!!!!)!

!!!!

Sample Covariance: !!" = !(!

!!! !!!!)(!!!!)!

Positive covariance indicates a positive linear association, negative covariance indicates an inverse or negative linear relationship, 0 covariance indicates no linear association. Correlation Co-efficient: Population correlation: ! = ! !!"!!!!

Sample correlation: ! = ! !!"!!!!!

Where: -1<!!, !<1 3 Probability 1 Conditional Probability: !!(!!!!!) != ! !!(!!!"#!!)!!(!) Joint Probability: !! !!!"#!! = !!! ! !!!! !

Mutually Exclusive: !!(!!!"!!) != !!!(!) !+ !!!(!)!Independence: !!(!!!!!) = !!(!)!! 4 Probability 2 Types of Random Variables: • Discrete (takes on a countable number of distinct

values) • Continuous (infinite number of values within

sample space)

Rules of expectation: • !(!"#$%&#%) != !!"#$%&#%!• !(!! + !!) != !!(!) !+ !!"#$%&#%!• !(!"#$%&#%!×!!) != !!!×!!(!)!• !"#(!"#$%&#%) != !0!• !"#(!! + !!"#$%&#%) != !!"#(!)!• !"#(!!×!!) != ! !!×!!"#(!)!

Binomial Probability:

P!(SSF)!= !!×!!!×!(1 − !),!!= !!!"#$%&!!"!!"##$!!$!×(1 − !)!"#$%&!!"!!"#$%&'(!

!

= !!×(1 − !)!!!!Uniform Random Variables:

P= !!× ! !!!!

5 The Normal Distribution Z – Scores:

! = ! − !!

Steps for standardising 1) Write down the notation and information that you know: !~!(!,!!), find values for the population mean (!), the population variance !! and the population standard deviation !. These values will be used to compute Z scores. 2) Write down what we want to know: E.g. !!(!! < !!! < !!) 3) Standardise the equation:

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