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### Statistics and Data Analysis

### Statistics and Data Analysis

Professor William Greene

Stern School of Business

IOMS Department

Department of Economics

Part 1 – Data Presentation

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 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

- 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

Discrete Data – US Crime Statistics; Counts of Occurrences.

Unordered Qualitative DataTravel Mode Between Sydney and Melbourne by 210 Travelers

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

Bond Ratings Movie Ratings

Problem with Ordered Survey Response Data

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

Very Unsatisfactory

Unsatisfactory

OK

Satisfactory

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

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

- In raw form
- Transformed to a visual form
- Summarized graphically
- Summarized statistically

Pie Chart

Pizza Pies Sold, by Type

A Box Plot Describes the Distributionof Values in a Set of Data

Hawaii

Box and Whisker Plot for House Price Listings

Making a Box Plot for Per Capita Income

Maximum=31136

3rdQuartile = 24933

Interquartile Range = IQR= 24933-21677 = 3256

Median=22610

1stQuartile = 21677

Minimum=17043

Box and Whisker Plot

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

Outliers

Smaller of (Maximum, Median + 1.5 IQR

75th Percentile

Interquartile range=IQR

Median

25th Percentile

Larger of (Minimum, Median – 1.5 IQR

HOG, pp. 39-43

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

… 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

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.

Summary

- 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)

Probability of Survival to Age 50, Female at BirthU.S. and 20 Other Wealthy Countries

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