Descriptive Statistics and Measures of Central Tendency

1. Taken together, all of the observations of a particular variable are called a distribution.
   • For example, the following visualizes real data from the 2010 General Social Survey:

We also talk about purely theoretical distributions invented by statisticians just for capturing ideas.

• One of the most important theoretical distributions is the "normal" distribution, perfectly symmetrical with a mean of 0 and some other features that make it really mathematically clean.

• A descriptive statistic is simply a numerical summary of a distribution.
• The two most important statistics describing a distribution are:
  1. The measure of central tendency – A numerical summary of a distribution’s center or most typical value
  2. The measure of dispersion – A numerical summary of the spread around a distribution's center.

Primer on Notation

• n = total number of observations in a sample
• Y = A vector of numerical values or just a list of observations on a variable
• Y = (Y1, Y2, Y3,...Yn) The big weird E just means sum all of the Y’s starting from the first (i = 1) up to the last (n).

\( \Sigma \)