Week 03 - From pictures to numbers

Prof. C. Austin Davis

Spring 2025

Roadmap for today

• Quiz
• Review at-home problems
• Rank statistics with US Income
• Mutated means with mental health data
• Spread with US DoS electricity usage
• Preview of next time

Quiz

Mean vs. median

• Mean balances a rod
• Median balances a string

At-home problems

Air quality in Delhi

Air quality in September

Air quality in January

Distributions display a lot of information

Distributions of real income

• What do we learn from this plot? A lot!
• The frequency of each income range across two years
• Typical values and the range
• Incomes under 90k less common in 2019 vs. 1980
• Incomes over 100k [much] more common in 2019 vs. 1980
• Inequality possibly increasing
• But if we have more than 2-3 groups, comparing distributions becomes unwieldy

Introducing summary statistics

• Typical values or “central tendency”
  • Mean
  • Median
• Range and spread
  • Percentiles
  • Min, max
  • Variance
• For categorical variables: [cross] tabulation

Central tendency and spread

Central tendency and spread

Income growth in the US

Our tools

• Documentation / codebook
• Frequency tables
  • The less exciting version of a histogram
  • Combining group_by(), summarize(), and n()
• Quantiles or percentiles
  • Definition
  • quantile() function
  # Mental health in a refugee setting

Density of PHQ-9 scores by community

Our tools

• Documentation
  • Questionnaire
  • Basic information document
• Creating new [binary] variables
  • mutate()
  • ifelse()

Energy use at US Embassies

Simulated energy use by month

Our tools

• Measuring the extremes
  • min()
  • max()
• Variance
  • Definition
  • var()

• Give example of the variance of ages around a dinner table where the guests are
  • A family
  • A group of friends from school

Preview of next time

Relationships between variables

Questions to ponder

How could you draw a line to summarize the relationship between math and language scores?