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Quantitative Business
Analysis (QBA 501)
Block 1 Slides
Dr. Keith Whittingham
Module Layout
QBA 501
DescriptiveStatistics
Probability &Distributions
StatisticalInference
RegressionAnalysis
Data, Tables& Graphs
SummaryData
Types of DataGraphical
TechniquesPivot Tables
Cent ral Location Rank and Order Dispersion Boxplot s
Learning Objectives -Displaying Data
Understand types of data
Create and interpret histograms
Understand relationships among datathrough scatterplots
Understand time series plots
Manipulating data with pivot tables
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Types of Data
There are several ways to categorizedata.
Numerical (quantitative) versuscategorical (qualitative)
Cross-sectional versus time series
Numerical Data
Quantitative values
Real numbers
Arithmetic calculations valid
Examples
Income levels
Product weights
Sales revenue
Production rate
Numerical Data
Can be Continuous or Discrete
Continuous
Infinite number of possible values
No gaps in possible values
Discrete
Gaps in possible values
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Categorical Data
Categorical quality of an observation
Mutually exclusive
Collectively exhaustive
Examples
Eye color blue, brown, etc
Size of customer small, medium, large
Categorical Data
Can be Nominal or Ordinal
Nominal
Named category as variable
Name can be a number
Ordinal
Category identifies ranked order of values
Observations
An observation is a member of thepopulation or sample.
Each row corresponds to anobservation.
In this data set, each person representsan observation.
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Variables
A variable is a specific attribute beingobserved/measured.
Each column represents a variable.
In this data set, each of the six piecesof information about a person is avariable.
Numerical versus Categorical -- continued
Some options for this example are to:
code Gender (1 for male and 2 for female)
uncode Opinion variable
categorize the Age variable as young (34or younger), middle aged (from 35-59) andelderly (60 or older).
There is no right or wrong way Dealers choice.
Cross-sectional versus TimeSeries
Cross-sectional dataAll variables measured at one point in time snap shot
Coding.xls is cross-sectional; otherexamples?
Time-series data Measure one or more variables at
successive points in time.
Time-series examples?
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Module Layout
QBA 501
DescriptiveStatistics
Probability &Distributions
StatisticalInference
RegressionAnalysis
Data, Tables& Graphs
SummaryData
Types of DataGraphical
TechniquesPivot Tables
Cent ral Location Rank and Order Dispersion Boxplot s
Frequency Tables andHistograms
Display how many observations fallwithin a category or range of values
Can be used for qualitative or quantitativevalues
Hard part is choosing categories(classes or bins)
Too many, or too few, and we losemeaningful information in the data.
Guidelines for bins/classes
Should be mutually exclusive
Should be collectively exhaustive
For Quantitative categories:
8-15 bins works best
Should have equal widths (roundnumbers better, e.g. 5, 10, 100, etc, )
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Frequency Distribution
Lets explore some common distributionshapes
Otis Elevators
Data consists of the diameter (ininches) of 400 elevator rails measuredby Otis Elevators.
The diameters range from a low ofapproximately 0.449 inch to a high ofapproximately 0.548 inch.
What type of distribution?
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Symmetric Histograms
A histogram is symmetric if it has asingle peak and looks approximately thesame to the left and right of the peak.
Bank Customer Arrivals
Data consists of the time betweencustomer arrivals - called interarrivaltimes - for all customers on a givenday.
What type of distribution?
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Positively Skewed Histograms
A histogram is positively skewed orskew ed to the right if it has a singlepeak and the values of the distributionextend much farther to the right of thepeak than to the left of the peak.
Accounting Midterm Grades
Data consists of the midterm grades fora large class of accounting students.
What type of distribution?
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Negatively Skewed Histograms
A histogram is negatively skew ed orskewed to the left if its longer tail ison the left.
Otis Elevators 2
Data consists of the diameters of allelevator rails produced on a single dayat Otis Elevators. Otis uses twomachines to produce elevator rails.
Too few bins
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Bimodal Distributions
Some histograms have two or morepeaks. This indicates that the datacomes from two or more distinctpopulations.
The result in this case is a bimodaldistribution.
Other multimodal distributions exist trimodal, etc.
Pie Chart
Cousin of the Histogram
Visualize frequency as a proportion ofthe entire data set.
Scatterplots
We are often interested in therelationship between two variables.
Plot a point for each observation, wherethe coordinates represent the values ofthe two variables.
The resulting graph is a scatterplot .
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Scatterplots
After constructing a scatterplot, we canexamine the scatter of points.
We look for any relationship between thetwo variables.
Direction: Is there a tendency for onevariable to move in concert with, or inopposition to, the other variable?
Strength: Are the points tightly clusteredaround an imaginary straight line? Or arethey more broadly scattered?
Time Series Plots
When we need to forecast future values of atime series, it is helpful to create a timeseries plot.
This is essentially a scatterplot, with the timeseries variable on the vertical axis and thetime itself on the horizontal axis.
Also, to make patterns in the data moreapparent, the points are usually connectedwith lines.
Analyzing a Time Series Plot
When looking at a time series plot weusually look for two things: Is there an observable trend or cycle? That
is, do the values of the series tend toincrease (an upward trend) or decrease (adownward trend) over time? Or cycle upand down?
Is there a seasonal pattern? For example,do the peaks or valleys for quarterly datatend to occur every fourth observation?
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Time Series Plots with twoVariables
Note that you can use different verticalscales for each variable.
This can yield time based relationshipsbetween variables in a manner similarto a scatterplot for cross-sectional data.
Module Layout
QBA 501
DescriptiveStatistics
Probability &Distributions
StatisticalInference
RegressionAnalysis
Data, Tables& Graphs
SummaryData
Types of DataGraphical
TechniquesPivot Tables
Cent ral Location Rank and Order Dispersion Boxplot s
Pivot Tables
One of Excels most powerful tools.
Pivot tables allow us to slice and dicethe data.
Statisticians often refer to the resultingtables as contingency tables orcrosstabs.
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Creating a Pivot Table
Position the cursor in the data range.
On the Insert ribbon, select the PivotTable drop-down.
Select whether you want a pivot tableor chart.
With the chart, you get the table for free.
Creating a Pivot Table --continued
Next specify the range of the data set.
Then specify where you want to placethe pivot table and/or chart.
Creating a Pivot Table --continued
PivotTable button on the Insert ribbon.
Source and destination dialog box.
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Creating a Pivot Table --continued
There are two ways to proceed in thenext step.
Firstly, you can check the box on the pivottable field list to populate the table.
Alternatively, you can drag the variablenames to the appropriate field area in thepivot table field list.
Blank Pivot Table
Creating a Pivot Table --continued
The Field List window the destination labelsdepend on whether you chose a table orchart
Here is the correspondence: Axis Fields correspond to Row Labels
Legend Fields correspond to ColumnLabels
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Pivot Table Summary
The best way to learn the full power ofPivot Tables is to get in and play.
The automatic link to the charts is verypowerful, you can jump back and forthto view the impact of your actions.
Finally, you can manipulate pivot chartsjust like any other Excel charts.
Module Layout
QBA 501
DescriptiveStatistics
Probability &Distributions
StatisticalInference
RegressionAnalysis
Data, Tables& Graphs
SummaryData
Types of DataGraphical
TechniquesPivot Tables
Cen tr al Locat ion Ran k an d Or derDispersion &
AssociationBoxplots
Learning Objectives -Displaying Data
Understand types of data
Create and interpret histograms
Understand relationships among datathrough scatterplots
Understand time series plots
Manipulating data with pivot tables
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