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Statistics and Data Analysis. Professor William Greene Stern School of Business IOMS Department Department of Economics. Statistics and Data Analysis. Part 1 – Data Presentation. Data Presentation Agenda. Data and Data Types Representing Data: pie chart, bar chart.

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statistics and data analysis

Statistics and Data Analysis

Professor William Greene

Stern School of Business

IOMS Department

Department of Economics

statistics and data analysis1

Statistics and Data Analysis

Part 1 – Data Presentation

data presentation agenda
Data Presentation Agenda
  • Data and Data Types
  • Representing Data: pie chart, bar chart.
  • Summarizing Data: box plot, histogram
    • Central tendency
    • Spread
    • Distribution (shape)
data a set of facts a picture of some aspect of the world
Data = A Set of FactsA picture of some aspect of the world

Pizza Sales by Type

What do the data tell you?

How can you use the information?

What additional information would make these data more informative?

data types and measurement
Data Types and Measurement
  • Quantitative
    • Discrete = count: Number of car accidents by city by time
    • Continuous = measurement: Housing prices
  • Qualitative
    • Categorical: Shopping mall, car brand, trip mode
    • Ordinal: Survey data on attitudes; “How do you feel about…?”

Strongly disagree  Disagree  Neutral  Agree  Strongly agree

Moody’s bond ratings: Aaa, Aa, A, Bbb, Bb, B, and so on.

  • Frameworks
    • Cross section
    • Time series

Ordered Qualitative DataGerman Health Satisfaction Survey; 27,326 individuals. On a scale from 0 to 10, how do you feel about your health?


Ordered Qualitative Outcomes

Bond Ratings Movie Ratings

problem with ordered survey response data
Problem with Ordered Survey Response Data

61 Stern Students’ Ranking of Subway Safety (1994)*

Very Unsatisfactory




Very Satisfactory

Is there an objective meaning to “3” on some standard scale?Does everyone’s “1” or “2” or “3” … mean the same thing?

* Jeff Simonoff: Data Presentation and Summary, pp. 3-4

quantitative vs qualitative data
Quantitative vs. Qualitative Data

Qualitative Data:

No units of measurement

Arithmetic manipulation is usually meaningless. The average of Air and Bus is not Train

Quantitative Data:

Units of measurement make sense. Arithmetic computations make sense.

representing data
Representing Data
  • In raw form
  • Transformed to a visual form
  • Summarized graphically
  • Summarized statistically
pie chart
Pie Chart

Pizza Pies Sold, by Type

data representation
Data Representation


Same data. Which is easier to understand?

a box plot describes the distribution of values in a set of data
A Box Plot Describes the Distributionof Values in a Set of Data


Box and Whisker Plot for House Price Listings

making a box plot for per capita income
Making a Box Plot for Per Capita Income


3rdQuartile = 24933

Interquartile Range = IQR= 24933-21677 = 3256


1stQuartile = 21677


box and whisker plot
Box and Whisker Plot

What is an outlier?Why do we believe a particular point is an outlier?


Smaller of (Maximum, Median + 1.5 IQR

75th Percentile

Interquartile range=IQR


25th Percentile

Larger of (Minimum, Median – 1.5 IQR

HOG, pp. 39-43

histogram for house price listings
Histogramfor House Price Listings

A histogram describes the sample data and suggests the nature of the underlying data generating process. Note the “skewness” of the distribution of listings.

HOG, pp. 16-18

distribution of house price listings
Distribution of House Price Listings

… shows up in the box and whisker plot. Note the long whisker at the top of the figure.

Asymmetry (skewness) in the histogram of listing prices…

a caution about graphical data summaries
A Caution About Graphical Data Summaries

Graphical tools can be very badly behaved when:

(1) The data have only a few observations.

(2) There are wild observations in the data set.

The box and whisker plot is distorted (and dominated) by one wildly errant observation.

  • What story does the data presentation tell?
    • Data in raw form tell no story.
    • Visual representation of data tells something about the data
  • Data reduction and summary representation: What do we learn?
    • Location
    • Spread
    • Shape of the distribution
  • What tool is most informative?
    • Reduction to a small number of features
    • Visual displays of data
      • Pie chart
      • Box and whisker plots
      • Histograms
      • Time series plots

“There are lies, damned lies and statistics.” (Benjamin Disraeli)