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Introduction to Statistics

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Objectives

  • How Can We Work With Data?
  • Finding Meaning in Data
  • Your Turn

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How Can We Work With Data?

We are inundated by data. Every. Single. Day.

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Consider the Datasets

  • For each dataset:
  • Describe it
  • Be as precise as possible
  • The gold standard is for someone else to recreate the data from your description
  • If that’s not possible, how close can you get to the standard?

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Dataset 1

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Dataset 2

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Dataset 3

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Differences in Datasets

  • All three datasets have different characteristics
  • What makes them similar?
  • What makes them different?
  • They were all randomly generated
    • Using what rules?
  • How can this be quantified?
  • Made describable?
  • These were random - there is no meaning 😢

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Discrete vs Continuous Data

  • Each of the datasets was discrete
    • Values can only take on specific values
    • Gaps exist in the data
  • Continuous data smoothly varies

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  • Examples
    • Stock market prices vs height of a baby

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Sampling

  • Continuous data can be sampled
    • Leads to discrete datasets
  • Sampling loses information from the underlying scenario
  • There are different types of sampling
    • Scales of samples
    • Biases introduced
    • More later

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Datasets

  • Dataset 1
  • Dataset 2
  • Dataset 3

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Alway Visualize!

  • Software tools will help!
  • TI-83
    • Used for IB exams
    • Practice with this even if you use other tools
    • Stats on the Graphing Calculator (also on class webpage)
  • Google Sheets
    • The most useful mathematical tool in your future!
  • Desmos and their statistics functions and tutorials
    • Limited to 1000 datapoints
  • GNU Octave (requires programming)
  • R at r-project.org for more sophisticated requirements (requires programming)

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Finding Meaning in Data

What do we see with these numbers?

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Some Real Data - World Water Stress Levels

  • What do you notice?
  • What do you wonder?
  • Capture the graph and main ideas
  • Discuss with neighbour
  • Full-sized picture

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World Water Stress Levels

  • Many high population cities might run out of water
  • Increased stress in part due to climate change
  • Water management can be improved with conservation, distribution systems, recycling, wetlands revitalization, less water-intensive crops
  • How can you use data like this to influence social policy?
  • Interactives including projections
  • Source

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Crime and Undocumented Immigrants

  • What do you notice?
  • What do you wonder?
  • Capture the graph and main ideas
  • Discuss with neighbour
  • Full-sized picture

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Crime and Undocumented Immigrants

  • Is there a correlation between crime and undocumented immigrants?
  • How accurate can the horizontal axis be?
    • The number of undocumented immigrants, by definition, will be hard to count
  • What does it mean that the data has outliers removed?
  • What narratives can be generated about this data
    • Are these narratives in conflict with each other?
  • Original NYTimes Article
  • Source

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Your Turn

What is important to you?

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Your Turn

  • Create a Google Doc
  • Title it “social phenomena”
  • Write down three social phenomena that are important to you or affecting your life
  • Take a stand!
    • Write an assertion about each phenomenon

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Your Turn

  • For each phenomenon:
    • Search for related data
    • What do you notice?
    • What do you wonder?
    • What is the purpose of the data?
    • How reliable is the data?
    • Does it increase or decrease support for your assertion?
  • Share your assertions and supporting data for the next class

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Credits

Special thanks to all the people who made and released these awesome resources for free:

  • Presentation template by SlidesCarnival
  • Photographs by Unsplash

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