Notesale: Turn your study into money

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Statistics, Data, and Statistical Thinking
Thursday, February 11, 2016

11:57 AM

The Science of Statistics

• Statistics: the science of data
○ Involves collecting, classifying, summarizing, organizing, analyzing, and
interpreting numerical and categorical information

Types of Statistical Applications in Business

• Sampling is when data is selected from some larger set of data whose
characteristics we wish to estimate
• Statistics involves
1
...
Drawing conclusions (making estimates, decisions, predictions, etc
...
e
...
g
...

the true data from the population)
○ We must put bounds on the estimation of error, which is a number that
the estimation error is not likely to exceed
A measure of reliability is a statement (usually quantified) about the degree of
uncertainty associated with a statistical inference

Four Elements of Descriptive Statistical Problems

The population or sample of interest
One or two more variables (characteristics of the population or experimental
units) that are to be investigated
Tables, graphs, or numerical summary tools
Identification of patterns in the data

Five Elements of Inferential Statistical Problems

The population of interest
One of more variables (characteristics of the population or experimental units)
that are to be investigated
The sample of population units
The inference about the population based on information contained in the
sample
A measure of reliability for the inference

Processes

• A process is a series of actions or operations that transforms inputs to outputs
○ A process produces or generates output over time
§ I
...
a drive-thru window
○ A manufacturing process uses a series of operations performed by people
and machines to convert inputs, such as raw materials and parts, to
finished products (the outputs)

• A process is a series of actions or operations that transforms inputs to outputs
○ A process produces or generates output over time
§ I
...
a drive-thru window
○ A manufacturing process uses a series of operations performed by people
and machines to convert inputs, such as raw materials and parts, to
finished products (the outputs)
• A process whose operations or actions are unknown or unspecified is called a
black box
○ The entire focus, therefore, is on the output of the process
○ If the output is numerical, the characteristic, or property, represented by
the numbers (e
...
sales, GDP, or stock prices) is typically the variable of
interest
§ A process whose output is already in numerical form necessarily
includes a measurement process as one of its subprocesses
○ If the output is not numeric, we use measurement processes to assign
numerical values to variables
○ Processes generate or create their output over time
• Any set of output (object or numbers) produced by a process is also called a
sample
○ Ex
...
The temperature (in degrees Celsius) at which each unit in a sample of
20 pieces of heat-resistant plastic bags melt
• Qualitative data are measurements that cannot be measured on a natural
numerical scale; they can only be classified into one of a group of categories
○ Ex
...


Collecting Data: Sampling and Related Issues

• Data is normally collected from a published source, a designed experiment, or
an observational study (e
...
a survey)
• A representative sample exhibits characteristics typical of those possessed by
the population of interest
• A simple random sample of n experimental units is a sample selected from the
population in such a way that every different sample of size n has an equal
chance of selection
○ Usually relies on a random number generator
• Stratified random sampling is typically used when the experimental units
associated with the population can be separated into two or more groups of
units, called strata, where the characteristics of the experimental units are more

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population in such a way that every different sample of size n has an equal
chance of selection
○ Usually relies on a random number generator
Stratified random sampling is typically used when the experimental units
associated with the population can be separated into two or more groups of
units, called strata, where the characteristics of the experimental units are more
similar within strata than across strata
○ Random samples within both strata, which are then combined to form the
complete sample
Cluster sampling samples natural groupings of experimental units first, then
collects data from all experimental units within each cluster
○ Ex

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