Introduction
What is Statistics?
Stat 226 – Introduction to Business Statistics I
Statistics is the science of collecting, describing and interpreting data
allowing for data-based decision making.
Spring 2009
Professor: Dr. Petrutza Caragea
Section A
Tuesdays and Thursdays 9:30-10:50 a.m.
“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 in
order to optimize resources, e.g.
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Introduction to Business Statistics I
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Introduction: Descriptive vs. Inferential
Predict the demand for products and services.
Check the quality of items manufactured in a facility.
Manage investment portfolios.
Forecast how much risk activities entail, and calculate fair and competitive
insurance rates.
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Introduction: Descriptive vs. Inferential
We distinguish between descriptive and inferential Statistics:
compared to 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:
Inferential Statistics
deals with the interpretation of data as well as drawing conclusions and
making generalizations based on data for a larger group of subjects.
Goals:
look for patterns
making data-based decisions
summarize and present data
generalizing information obtained from descriptive analysis to a larger
group of individuals
quick information
compare several groups, i.e. one can easily look for differences and
similarities
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Introduction to Business Statistics I
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Introduction: Descriptive vs. Inferential
Introduction: Population vs. Sample
Example: Before movies are released they are previewed by a selected
audience. Assume 200 people are asked to provide an overall rating for a
movie yielding the following responses:
Population
Examples:
24% very satisfied
all ISU students currently enrolled
26% satisfied
all Audi A6 vehicles manufactured in a year
33% in between
all customers banking with Wells Fargo
12% dissatisfied
Sample
5% very dissatisfied
⇒ 24% of the 200 previewers were very satisfied with the movie – this is
a descriptive statement based on a sample of 200 previewers.
⇒ 24% of all people who will see the movie will be very satisfied with the
movie – this is an inferential statement for the entire population of
individuals.
Stat 226 (Spring 2009, Section A)
The population in a study is the entire group of individuals or subjects about which
we want to gain information.
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Introduction: Population vs. Sample
A sample is a subgroup (or part) of a population from which we obtain information in
order 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
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Introduction: Populations vs. Sample
Need to be careful, the terms population and statistics are relative.
Consider all college students in the US, then all ISU students are no longer
the population of interest but rather a sample.
⇒ Clearly formulate what the population of interest is!
When using numerical summaries to describe samples or populations we
need 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
It is important to distinguish between a population parameter and a
sample statistic.
A parameter is a numerical summary of a population. Populations
consist typically of too many individuals, so that these can never be
observed. For example, it would be impossible to know the average
summer earnings of all university students. This would require us to
identify, find, and question thousands of students. Therefore we will hardly
ever know the true parameter value of a population.
It is however feasible to select a sample of 100 students (using proper
randomization) and then the average earning of these 100 students could
be computed. Any numerical measure computed from a subset of the
population (typically a sample) is a statistic and can be observed.
24% of all people going to see the movie: 24% – parameter
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Introduction: Parameter vs. Statistic
Introduction: Individuals and Variables
some more definitions...
Parameter
is a numerical summary for the entire population. It typically remains
unknown as we cannot observe the entire population. We will use the
information based on the data such as a sample mean to get an idea what
the value of the unknown population parameter is — this process is
inferential.
Statistics
are numerical summaries (e.g. an average) that are obtained from real
data, we can actually observe a statistic — statistics are descriptive.
Stat 226 (Spring 2009, Section A)
Introduction to Business Statistics I
Introduction
Individuals
Individuals are subjects/objects of the population of interest; can be
people but also business firms, common stocks or any other object that we
want to study. Examples?
A Variable
A variable is any characteristic of an individual that we are interested in. A
variable typically will take on different values for different individuals.
Examples?
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Introduction: Kinds of variables
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Introduction: Kinds of variables
Categorical variables
Individuals can be placed into one of several categories.
We distinguish nominal and ordinal variables.
Quantitative variables
Quantitative variables take numerical values for which arithmetic
operations such as adding and averaging make sense, e.g.
nominal: no order possible
gender
religion
race
colors
height of a person
weight of a person
temperature
time it takes to run a mile
ordinal: order is possible
currency exchange rates
grades
educational degrees
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Introduction
Distribution
The distribution of a variable describes WHAT values the variable takes
and HOW often it takes these values.
Depending on the type of the data (categorical or quantitative) we need to
use different graphical and numerical tools to analyze and summarize the
data at hand.
We will start by describing data graphically:
bar graphs, pie charts and pareto charts can be used to graphically
summarize categorical data.
a common graphical display for quantitative data is a histogram.
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