Statistical Foundations for Trading: Distributions, Volatility, and Correlation
Summary
This introductory guide explains descriptive statistics and probability concepts using daily Apple stock data. It defines mean, mode, and median, then introduces range and standard deviation as ways to describe price levels and dispersion. It distinguishes discrete probability mass functions from continuous probability density functions and uses dice outcomes and student heights as examples.
The discussion connects standard deviation to volatility and Bollinger Bands, and suggests that a move above an upper band can be treated as a breakout signal. It also introduces histograms and the normal distribution, then discusses correlation as a measure of linear association that does not establish causation and may miss nonlinear relationships. The examples are educational rather than a tested strategy; price-level statistics and a normality assumption may not characterize return behavior reliably, and no out-of-sample performance evidence is provided.
Key ideas
- The mean, median, and mode summarize data in different ways, with the median less sensitive to extreme observations.
- Probability mass functions describe discrete outcomes, while density functions represent continuous outcomes.
- Standard deviation measures dispersion and is used in volatility measures and Bollinger Bands.
- Histograms show the frequency distribution of observed values.
- Correlation captures linear association but does not prove causation or reliably reveal nonlinear relationships.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.