Data Scales and Summary Statistics
From Ian Stark
This lecture gives 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.
The lecture covers these specific items.
- 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