Lecture 17: Data Scales and Summary Statistics

Title slideThis morning’s 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.

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? Is there more than one possible way the drawing might come out?

Links: Slides for Lecture 17; Video of Lecture 17


Two books for learning about statistics, what they can do, and how to use them effectively:

Two more for reading about statistics in the real world. Both easy to digest and recommended for interest. Get them out of the library, buy a copy, or read online.

The Copernican Principle

  • Wikipedia on the Copernican Principle in its appropriately cosmological sense.
  • A Grim Reckoning. Article by J. Richard Gott III on his application of this to everything, up to and including the end of civilization. (May require EASE login; this is an article from the University’s paid subscription to New Scientist.)
  • How to Predict Everything. Timothy Ferris, New Yorker, 12 July 1999. This is the article about Gott in which he discusses the performance of plays on Broadway. It’s available online, but only to subscribers.

Grade Scales

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