Lecture 17: Data Scales and Summary Statistics

This lecture gave a general overview of statistics and their role in analysing quantities of data. Most of the technical constructions — mean, median, mode, standard deviation — are probably familiar to many, but the setting for their application and the computational context may not be.

Mathematical statistics turns out to be a tool of exceptional power for distilling information from data, with computer assistance having particular impact where there are large quantities of data, or very thinly-spread information.

One recent notable example is the announcement yesterday from the BICEP2 project of evidence for gravitational waves and inflation in the very early universe, identified by traces in the twisting polarisation of the cosmic microwave background radiation. This is a significant scientific discovery, dependent on sophisticated and computation-heavy resampling analyses of a mass of observational data.

Specific items covered in this lecture were:

  • Data scales: qualitative and quantitative; categorical, ordinal, interval and ratio.
  • Individual statistics: mode, median, mean, variance, standard deviation. When you really should use a median, and the seductive danger of the mean.
  • Sampling: estimating statistics of a large population from a small sample; mean, variance and standard deviation.

Finally, a problem: how to draw this example of self-descriptive statistics? Which frame do you begin with? Could you do it without the aid of a computer?

Links: Slides; Recording

Books

Two books for learning about statistics, and to refer to when applying them:

Two more for reading about statistics in the real world. Both easy to digest and recommended for interest.

Finding Gravitational Waves at the Start of the Universe

Here are an assortment of links to the BICEP2 announcements yesterday, explanations and analyses.

Grade Scales

Current Danish grading system; the 13-point scale described in the lecture; and the magnificent Extended ├śrsted scale.

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