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Lecture 2: Displaying distributions

AR de LeonDepartment of Mathematics and Statistics

University of Calgary

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“At least 1.75 billion reasons to go into statistics”

Prof. Susan A. MurphyDepartment of StatisticsUniversity of Michigan

“Every time we have gured out a new way to collect data, there is

an explosion in both the need for statisticians and great excitement for what can be done with the data...We have all these new ways to collect data via wearable sensors, the Internet, genetics, astronomy,and more, and it’s creating all kinds of new problems for data scientists to solve.”


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“Quantifying global international migration ows”

Science, March 2014 Fall 2015 AR de Leon U of Calgary Sept 11, 2015 3/26

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4/26Fall 2015 AR de Leon U of Calgary Sept 11, 2015 4/26

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On measurement

Denition

We measure a property of a person or thing when we assign a numberto represent the property.

Some instrument is often used to make a measurement.

We can usually choose in what unit to record our measurements.Denition

A variable is the numerical result of measurement; it takes different valuesfor people or things that differ in the property we are measuring.

Denition

A variable is a valid measure of a property if it is a relevant/appropriaterepresentation of that property.


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Histograms are not unique!

All 3 histograms are of the same data created with the same width 10

for the classes but with different lower class limits for the rst class.Fall 2015 AR de Leon U of Calgary Sept 11, 2015 14/26

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Histogram examples

The right-hand histogram is right-skewed , suggesting that Shakespeare’splays contain many short words (up to six letters) and few very long words.


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Distribution of heights of OKCupid users


“ i l ll i li d i ” ( O d 20 0)

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“Lies people tell in online dating” ( OKTrends , 2010)


M l f l i OKC id ( D l 2014)

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Males vs. females in OKCupid ( Dataclysm , 2014)

“Two-thirds of male messages go to the best-looking third of women. So basically, guys are ghting each other 2-for-1 for the absolute best-rated females.”

“Women rate an incredible 80% of guys as worse-looking than

medium.” Fall 2015 AR de Leon U of Calgary Sept 11, 2015 20/26

I ’ l !

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It’s not always pretty!


O tli

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Outliers


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A histogram you may nd personally interesting

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A histogram you may nd personally interesting...


Displays for categorical data

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Displays for categorical data

Bar charts of OKCupid users by categorical variables sex (male of female) and by sexual orientation (straight, bisexual or gay).

A mosaic plot summarizing OKCupidusers by both sex and sexualorientation .


Practice exercises

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Practice exercises

Exercise 1.36

Exercise 1.38Exercise 1.39

Exercise 1.41

Exercise 1.43Exercise 1.46


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