Stat 226 -- Introduction to Business Statistics Ipcaragea/S226S09/Notes/lecture.notes... · Stat 226 – Introduction to Business Statistics I Spring 2009 Professor: Dr. Petrutza

Stat 226 – Introduction to Business Statistics I

Spring 2009Professor: Dr. Petrutza Caragea

Section ATuesdays and Thursdays 9:30-10:50 a.m.

Introduction

Stat 226 (Spring 2009, Section A) Introduction to Business Statistics I Introduction 1 / 13

Introduction

What is Statistics?

Statistics is the science of collecting, describing and interpreting dataallowing for data-based decision making.

“I like to think of statistics as the science of learning from data...”(Jon Kettenring, ASA President 1997)

In Business and Industry Statistics can be used to quantify unknowns inorder to optimize resources, e.g.

1 Predict the demand for products and services.

2 Check the quality of items manufactured in a facility.

3 Manage investment portfolios.

4 Forecast how much risk activities entail, and calculate fair and competitiveinsurance rates.


Introduction

What is Statistics?









Introduction

What is Statistics?









Introduction: Descriptive vs. Inferential

We distinguish between descriptive and inferential Statistics:

Descriptive Statistics

is the collection, presentation and description of data in form of graphs,tables and numerical summaries such as averages, variances etc.

Goals:

look for patterns

summarize and present data

quick information

compare several groups, i.e. one can easily look for differences andsimilarities



We distinguish between descriptive and inferential Statistics:

Descriptive Statistics

is the collection, presentation and description of data in form of graphs,tables and numerical summaries such as averages, variances etc.

Goals:

look for patterns

summarize and present data

quick information

compare several groups, i.e. one can easily look for differences andsimilarities



compared to inferential statistics:

Inferential Statistics

deals with the interpretation of data as well as drawing conclusions andmaking generalizations based on data for a larger group of subjects.

Goals:

making data-based decisions

generalizing information obtained from descriptive analysis to a largergroup of individuals



Example: Before movies are released they are previewed by a selectedaudience. Assume 200 people are asked to provide an overall rating for amovie yielding the following responses:

24% very satisfied

26% satisfied

33% in between

12% dissatisfied

5% very dissatisfied

⇒ 24% of the 200 previewers were very satisfied with the movie – this isa descriptive statement based on a sample of 200 previewers.

⇒ 24% of all people who will see the movie will be very satisfied with themovie – this is an inferential statement for the entire population ofindividuals.




24% very satisfied

26% satisfied

33% in between

12% dissatisfied







24% very satisfied

26% satisfied

33% in between

12% dissatisfied





Introduction: Population vs. Sample

Population

The population in a study is the entire group of individuals or subjects about whichwe want to gain information.

Examples:

all ISU students currently enrolled

all Audi A6 vehicles manufactured in a year

all customers banking with Wells Fargo

Sample

A sample is a subgroup (or part) of a population from which we obtain information inorder to draw conclusions about the entire population.

Examples:

every 5th ISU students currently enrolled

all Audi A6 vehicles manufactured on a single day

100 randomly chosen customers banking with Wells Fargo



Population

The population in a study is the entire group of individuals or subjects about whichwe want to gain information.

Examples:

all ISU students currently enrolled

all Audi A6 vehicles manufactured in a year

all customers banking with Wells Fargo

Sample

A sample is a subgroup (or part) of a population from which we obtain information inorder to draw conclusions about the entire population.

Examples:

every 5th ISU students currently enrolled

all Audi A6 vehicles manufactured on a single day

100 randomly chosen customers banking with Wells Fargo



Need to be careful, the terms population and statistics are relative.

Consider all college students in the US, then all ISU students are no longerthe population of interest but rather a sample.

⇒ Clearly formulate what the population of interest is!

When using numerical summaries to describe samples or populations weneed to distinguish between a so-called statistic and a parameter:

any numerical summary describing a sample is called a statistic

any numerical summary describing a population is called a parameter

Example: movie preview

24% of the 200 previewers: 24% – statistic

24% of all people going to see the movie: 24% – parameter


Introduction: Populations vs. Sample

It is important to distinguish between a population parameter and asample statistic.

A parameter is a numerical summary of a population. Populationsconsist typically of too many individuals, so that these can never beobserved. For example, it would be impossible to know the averagesummer earnings of all university students. This would require us toidentify, find, and question thousands of students. Therefore we will hardlyever know the true parameter value of a population.

It is however feasible to select a sample of 100 students (using properrandomization) and then the average earning of these 100 students couldbe computed. Any numerical measure computed from a subset of thepopulation (typically a sample) is a statistic and can be observed.


Introduction: Parameter vs. Statistic

Parameter

is a numerical summary for the entire population. It typically remainsunknown as we cannot observe the entire population. We will use theinformation based on the data such as a sample mean to get an idea whatthe value of the unknown population parameter is — this process isinferential.

Statistics

are numerical summaries (e.g. an average) that are obtained from realdata, we can actually observe a statistic — statistics are descriptive.


Introduction: Parameter vs. Statistic

Parameter

is a numerical summary for the entire population. It typically remainsunknown as we cannot observe the entire population. We will use theinformation based on the data such as a sample mean to get an idea whatthe value of the unknown population parameter is — this process isinferential.

Statistics

are numerical summaries (e.g. an average) that are obtained from realdata, we can actually observe a statistic — statistics are descriptive.


Introduction: Individuals and Variables

some more definitions...

Individuals

Individuals are subjects/objects of the population of interest; can bepeople but also business firms, common stocks or any other object that wewant to study. Examples?

A Variable

A variable is any characteristic of an individual that we are interested in. Avariable typically will take on different values for different individuals.Examples?


Introduction: Individuals and Variables

some more definitions...

Individuals

Individuals are subjects/objects of the population of interest; can bepeople but also business firms, common stocks or any other object that wewant to study. Examples?

A Variable

A variable is any characteristic of an individual that we are interested in. Avariable typically will take on different values for different individuals.Examples?


Introduction: Kinds of variables

Categorical variables

Individuals can be placed into one of several categories.

We distinguish nominal and ordinal variables.

nominal: no order possible

genderreligionracecolors

ordinal: order is possible

gradeseducational degrees




Individuals can be placed into one of several categories.We distinguish nominal and ordinal variables.































Quantitative variables

Quantitative variables take numerical values for which arithmeticoperations such as adding and averaging make sense,

e.g.

height of a person

weight of a person

temperature

time it takes to run a mile

currency exchange rates



Quantitative variables

Quantitative variables take numerical values for which arithmeticoperations such as adding and averaging make sense, e.g.

height of a person

weight of a person

temperature

time it takes to run a mile

currency exchange rates


Introduction

Distribution

The distribution of a variable describes WHAT values the variable takesand HOW often it takes these values.

Depending on the type of the data (categorical or quantitative) we need touse different graphical and numerical tools to analyze and summarize thedata at hand.

We will start by describing data graphically:

bar graphs, pie charts and pareto charts can be used to graphicallysummarize categorical data.

a common graphical display for quantitative data is a histogram.


Introduction

Distribution

The distribution of a variable describes WHAT values the variable takesand HOW often it takes these values.

Depending on the type of the data (categorical or quantitative) we need touse different graphical and numerical tools to analyze and summarize thedata at hand.

We will start by describing data graphically:

bar graphs, pie charts and pareto charts can be used to graphicallysummarize categorical data.

a common graphical display for quantitative data is a histogram.


Documents

Stat 226 -- Introduction to Business Statistics Ipcaragea/S226S09/Notes/lecture.notes... · Stat 226 – Introduction to Business Statistics I Spring 2009 Professor: Dr. Petrutza