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ECON1203: Business and Economics Statistics University of New South Wales 1 Introduction to Statistics 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 Variables Discrete (cannot include every possible observation within sample space) Continuous (can include all possible observations within sample space) Qualitative (in terms of words, e.g. categories) Quantitative (in terms of numbers) Ordinal data (qualitative data with rankings) Time series data (references data with time) Descriptive statistics (summarise data in terms of numerical values) Inferential statistics (gives inferences about the populations) Ogives – Captures information about cumulative Pie Charts - circular display of data, where the whole pie represents 100%

Bar Chart - Easy to read and accurately interpret Pareto Graph – Bar Chart in descending order 2 Measures of Location, Variation and Association 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 Data Sampling Types of Sampling:

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

Steps in Statistical Analysis

• Define and understand the problem at hand • Collect data on the variable you want to study • Analyse the data through descriptive

measures (statistics), using that information infer something about the parameter.

• Communicate results to the public and await feedback

4 Probability Conditional Probability: !!(!!!!!) != ! !!(!!!"#!!)!!(!) Joint Probability: !! !!!"#!! = !!! ! !!!! !

Mutually Exclusive: !!(!!!"!!) != !!!(!) !+ !!!(!)!Independence: !!(!!!!!) = !!(!)!! 5 Random Variables Types of Random Variables: • Discrete (takes on a countable number of distinct

values) • Continuous (infinite number of values within

sample space)

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