Week 2 · Distribution, variance and its applications

Density and cumulative distributions, variance, quantiles, z-scores and the WHO growth standards

The week moves from describing a variable’s centre to describing its whole distribution. It ends with two applications that come back later in the course: measuring child stunting against the WHO length-for-age standard, and the Datasaurus, which shows why a univariate summary is never enough.

The full deck

Material WS 2024/25 WS 2023/24
🖥 Interactive slides Week 02. Distribution, Variance and its applications not rendered (sources were revised for 2024/25)
📄 PDF from Ilias Week 02. Distribution, Variance and its applications.pdf · 72 pages · added 21 Oct 2024 Week 02. Distribution, Variance and its applications.pdf · 72 pages · added 11 Dec 2023
💻 Source mk68-02-slides.qmd mk68-02-slides.qmd

In 2024/25 the deck was assembled from four parts, each of which is also rendered on its own:

Part Interactive slides Source
Distribution 🖥 Open 💻 mk68-02-slides-distributions.qmd
Variance 🖥 Open 💻 mk68-02-slides-variance.qmd
Quantiles 🖥 Open 💻 mk68-02-slides-quantiles.qmd
Income deciles example 🖥 Open 💻 mk68-02-slides-example-1.qmd

What the deck covers

  • Distribution: symmetric and non-symmetric distributions, extreme and influential observations; from a density to a cumulative distribution; the cumulative distribution of income; applications to income inequality and the Lorenz curve, with homework examples.
  • Variance: population versus sample variance, the standard deviation, and why distributions with the same standard deviation can look very different.
  • Quantiles: quartiles and deciles for normal and non-normal distributions; income deciles; an example on inequality, taxes and subsidies; robust versus non-robust measures of spread; matching distributions to box plots.
  • Application of variance in descriptive analysis: measuring stunting; the WHO length/height-for-age standard, how it is built and summarised, and following one boy’s development against it.
  • The (standard) normal distribution: the z-score, why it is needed, standardisation, and exam examples on determining stunting status.
  • When univariate analysis is not enough: the Datasaurus, a synthetic dataset whose univariate summaries hide everything.
  • Reading before Week 4, homework examples on z-scores, variance and the normal distribution, a pointer to Our World in Data on income inequality, and the key concepts checklist.

Data used

Where the course goes next

← Week 1 · Introduction. Descriptive statistics · → Week 3 · Bi-variate data. Correlation and causation