Introduction to Data Analysis and Decision Making

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Introduction to Data Analysis and Decision Making
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Data Analysis

• Describing data and datasets
• Making inferences from data and datasets
• Searching for relationships in data and datasets

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Decision Making

• Optimization
• Decision analysis with uncertainty
• Sensitivity Analysis

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Uncertainty

• Measuring uncertainty
• Modeling and simulation

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What is Management Science?

• Logical, systematic approach to decision making
  using quantitative methods.
• Science ?Scientific methods used to solve
  business related problems.
• Goal for this class logically approach and
  solve many different problems.

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Management Science Approach to Problem Solving

• Observation
• Definition of the Problem
• Constructing the Model
• Solving the Model/problem
• Implementation of Solution
• (process is never really complete)

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Observation

• Identify the problem
• Problem does not imply that there is something
  wrong with the process
• Problem could imply need for improvement

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Definition of the Problem

• Clearly define problem
• Prevents incorrect/inappropriate solution
• Listing goals could be helpful

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Constructing the Model

• Represents the problem in abstract form
• Schematic, scale, mathematical relationship
  between variables (equation)
• Ex Income Hours Worked Pay

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Components of the Model

• Variable/Decision Variables
• Independent
• Dependent
• Objective Function
• Parameter
• Constraints

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Model Solution

• Same as solving the problem
• Ex Z 20X 5X
• subject to
• 4X 100
• Solution
• X25 ?Z 375

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Implementation of Solution

• Solution aids us in making a decision but does
  not constitute the actual decision making.

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Example

• Blue Ridge Hot Tubs manufactures and sell hot
  tubs. The company needs to decide how many hot
  tubs to produce during the next production cycle.
  The company buys prefabricated fiberglass hot
  tub shells from a local supplier and adds pump
  and tubing to the shells to create his hot tubs.
  The company has 200 pumps available. Each hot
  tub requires 9 hours of labor. The company
  expects to have 1,566 production labor hours
  during the next production cycle. A profit of
  350 will be earned on each hot tub sold. The
  company is confident that all of the hot tubs
  will sell. The question is, how many should be
  produced if the company wants to maximize profits
  during the next production cycle?

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Msci Approach to Problem Solving

• Problem Determine of hot tubs to produce
• Definition Maximize profit within the
  constraints of the labor hours and materials
  available
• Model Max Z 350X
• subject to
• 9X ? 1,566 labor hours
• Solution X 174 Z 350(174) 60,900
• Implementation Recommend making 174 hot tubs

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A Generic Mathematical Model
Y f(X1, X2, , Xk)
Where
Y dependent variable (a bottom line performance
measure) Xi independent variables (inputs
having an impact on Y) f(.) function defining
the relationship between the Xi and Y
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Categories of Mathematical Models
Model Independent OR/MS Category Form of
f(.) Variables Techniques
Prescriptive known, known or under LP, Networks,
IP, well-defined decision makers CPM, EOQ,
NLP, control GP, MOLP Predictive unknown, know
n or under Regression Analysis,
ill-defined decision makers Time Series
Analysis, control Discriminant
Analysis Descriptive known, unknown
or Simulation, PERT, well-defined uncertain Queue
ing, Inventory Models
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Example Spring Mills

• 280 observations
• Three variables per observation
• Relatively large dataset

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Background Information

• Spring Mills produces and distributes a wide
  variety of manufactured goods. It has a large
  number of customers.
• Spring Mills classifies these customers as small,
  medium, or large, depending on the volume of
  business each does with them.
• Recently they have noticed a problem with
  accounts receivable. They are not getting paid by
  their customers in as timely a manner as they
  would like. This obviously costs them money.

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RECEIVE.XLS

• Spring Mills has gathered data on 280 customer
  accounts.
• For each of these accounts the data set lists
  three variables
• Size - The size of the customer (coded 1 for
  small, 2 for medium, 3 for large).
• Days - The number of days since the customer was
  billed.
• Amount - The amount the customer owes.
• What information can we obtain from this data?

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Summary Measures for Combined Data
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Scatterplot Amount vs DaysAll Customers
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Scatterplot Amount vs DaysSmall Customers
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Scatterplot Amount vs DaysMedium Customers
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Scatterplot Amount vs DaysLarge Customers
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Analysis -- continued

• There is obviously a lot going on here and it is
  evident form the charts. We point out the
  following
• there are considerably fewer large customers than
  small or medium customers.
• the large customers tend to owe considerably more
  than small or medium customers.
• the small customers do not tend to be as long
  overdue as the large and medium customers.
• there is no relationship between Days and Amount
  for the small customers, but there is a definite
  positive relationship between these variables for
  the medium and large customers.

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Findings

• If Spring Mills really wants to decrease
  receivables, it might want to target the
  medium-sized customer group, from which it is
  losing the most interest.
• Or it could target the large customers because
  they owe the most on average.
• The most appropriate action depends on the cost
  and effectiveness of targeting any particular
  customer group. However, the analysis presented
  here gives the company a much better picture of
  whats currently going on.

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Modeling and Models

• Graphical models
• Algebraic models
• Spreadsheet models

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The Modeling Process

• Define the problem
• Collect and summarize data
• Formulate a model
• Verify the model
• Select one or more suitable decisions
• Present the results to the organization
• Implement the model and update through time

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Describing DataThe Basics
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Descriptive vs Inferential Statistics

• Descriptive statistics
• The process of applying a method of analysis to a
  set of data in order to better understand the
  information contained within.
• Inferential statistics
• Using a (sub)set of data (a sample) to predict
  behavior of a larger set of data (the population).

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Population

• Definition
• Set of existing units (usually people, objects,
  transactions, or events) or
• Every element in a group that is the subject of
  interest
• Depends upon the problem or situation
• Examples
• College students, Honda Accords, cash sales

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Population Parameters and Sample Statistics
A population parameter is number calculated from
all the population measurements that describes
some aspect of the population. The population
mean, denoted ?, is a population parameter and is
the average of the population measurements. A
point estimate is a one-number estimate of the
value of a population parameter. A sample
statistic is number calculated using sample
measurements that describes some aspect of the
sample.
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Measures of Central Tendency
Mean, ? The average or expected value Median,
Md The middle point of the ordered
measurements Mode, Mo The most frequent value
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The Mean
Population X1, X2, , XN
m
Population Mean
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Relationships Among Mean, Median and Mode
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Variables

• Definition
• Characteristic or property of an individual
  population unit
• Particular characteristics or properties may vary
  among units in a population
• Examples
• Starting salary of MBA college graduates
• Price of peanut butter at grocery stores

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Measurement

• Definition
• The process of quantifying information
• Quantitative variables
• Test scores, product and process measurements,
  survey results, etc.
• Qualitative variables
• Product rating, arbitrary scales, etc.

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Sample

• Definition
• Subset of the units of the population
• Example
• 100 GPAs from all finance majors
• Tool wear on 3 machines out of 45 machines
• Notes
• A random sample implies no statistical bias
• A census includes all population members

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Statistical Inference

• Definition
• Estimation, prediction, or other generalizations
  about a population based on information contained
  in a sample.
• Example
• Based on a 5 year sample of similar weather
  patterns, predicting the chance of rain today.

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Reliability of the Inference

• Four items discussed thus far allow for
  statistical inference
• A population, variable(s) of interest, a sample,
  and an inference.
• Fifth Item A measure of the reliability of the
  inference.
• How good the inference is, i.e. how much
  confidence can we place in the inference?

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Example

• The approval rating of the President what does
  it really mean?
• Uses a sample from the population to infer the
  percentage of the population that approves of his
  overall performance.
• Implies that 55 of the population approves of
  the presidents performance plus or minus 5,
  i.e. between 50 and 60.

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Process Statistics

• A process transforms inputs into outputs
• A manufacturing process which transforms aluminum
  sheet into aluminum cans.
• A service process which offers financial advice
  based on a customers input.
• Samples are obtained from a process and
  statistical procedures can then be applied to
  make inferences about the process itself.

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Sampling a Process
Process A sequence of operations that takes
inputs (labor, raw materials, methods, machines,
and so on) and turns them into outputs (products,
services, and the like.)

A process is in statistical control if it
displays constant level and constant variation.
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Types of Data

• Data can be classified into four types
• Nominal
• Ordinal
• Interval
• Ratio

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Nominal Data

• Classify the members of the sample into
  categories (Categorical Data).
• Examples
• An individuals religious affiliation
• Gender of applicants
• An individuals political party affiliation
• No mathematical properties, i.e. numerical values
  are only codes.

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Ordinal Data

• Units of the sample can be ordered with respect
  to the variable of interest.
• Examples
• Size of rental cars.
• Ranking of microbrews with respect to taste.
• Ranking of consumer preferences for a product.
• No mathematical properties in that the difference
  between ranking values is meaningless.

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Interval Data

• Sample measurements enable comparisons between
  members of the sample, i.e. the differences
  between samples has meaning.
• Examples
• Temperature or pressure readings.
• Machine speeds
• Can add and subtract but cannot multiply or
  divide origin has no meaning.

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Ratio Data

• Equal distance between numbers imply equal
  distances between the values of the
  characteristic being measured, i.e. zero
  represents the absence of the characteristic
  being measured.
• Examples
• Sales revenue for a product or service.
• Unemployment rate.

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Classes of Data

• Data can be classified as either being
• Qualitative data - nominal, ordinal, or
• Quantitative data - interval, ratio.
• Numerical data can also be discrete (countable)
  or continuous.
• Spreadsheet (or Database)
• Variable (or Field)
• Observation (or Record)

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Describing DataGraphs and Tables
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Displaying Data

• For both Qualitative and Quantitative Data
• Pie Charts
• Bar Graphs (Bar Charts)
• Histograms
• Frequency Tables
• Stem and Leaf Diagrams

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Pie Chart Example

• 1999 Cigarette Sales (in billions) by company
• Philip Morris, 211.8
• Reynolds, 189.7
• Brown and Williamson, 69.1
• Lorillard, 48.6
• American, 43.9
• Liggett, 29.8

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Bar Graph Example

• 1999 Cigarette Sales (in billions) by company
• Philip Morris, 211.8
• Reynolds, 189.7
• Brown and Williamson, 69.1
• Lorillard, 48.6
• American, 43.9
• Liggett, 29.8

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Histogram Example

• Percentage of Sales Revenue spent on Advertising
  for a sample of 35 Fortune 500 companies
• 1 to 3 (4)
• 3 to 5 (9)
• 5 to 7 (11)
• 7 to 9 (8)
• 9 to 11 (3)

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Measurement Classes

• Intervals are called measurement classes
• A count of the members of a measurement class is
  the frequency.
• The proportion of members in a measurement class
  is the relative frequency. For a given interval,
  this proportion is calculated by dividing the
  frequency of the measurement class by the sample
  size.

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Relative Frequency

• Sample

• Frequency Table
• Divide range into intervals of equal size.
• Count the number of sample members that fall
  within the ranges.

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Relative Frequency Histogram Example

• Percentage of Sales Revenue spent on Advertising
  for a sample of 35 Fortune 500 companies
• 1 to 3 (4/350.114)
• 3 to 5 (9/350.257)
• 5 to 7 (11/350.314)
• 7 to 9 (8/350.229)
• 9 to 11 (3/350.086)

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Stem and Leaf Diagrams

• Data is displayed graphically
• The stem is the portion of the data to the left
  of the decimal point.
• The leaf is the portion of data to the right of
  the decimal point.
• Graphical representation much like Histogram.

• From our previous data

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The Effect of Measurement Class Size on a
Histogram

• A Histogram showing greater detail can be
  obtained by
• Decreasing class size (which increases the number
  of classes), or
• Increasing sample size (which increases the
  number of members in each class).

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Excel and StatPro Add-in Demonstration

• Frequency tables
• Histograms
• Scatterplots
• Time series plots