Topic 3: Distributions & Quantiles

Hey! If you’ve ever looked at a Normal Distribution curve or a list of R-functions and felt a bit lost, I totally get it. I wrote these notes to turn those confusing textbook chapters into something I could actually use for my own assignments and exams. These are my handwritten, step-by-step guides that take the mystery out of how data actually behaves. Topics covered: 1. The Binomial Distribution: Detailed criteria for binomial trials, including fixed trials, independence, and binary outcomes, alongside the full PMF derivation. 2. Computational Statistics in R: Direct syntax and practical examples for using dbinom and pbinom functions to calculate exact and cumulative probabilities. 3. The Normal Distribution: Analysis of the Bell Curve, Mean, and Standard Deviation, featuring the 68-95-99.7 Empirical Rule and Z-score standardization. 4. Quantiles and Sample Percentiles: A methodology for finding Medians, Quartiles (Q1, Q2, Q3), and the Interquartile Range for both even and odd datasets. 5. Normal Quantile Plots (QQ Plots): Instructions on arranging observed data and plotting it against normal quantiles to visually check for data normality. 6. Data Interpretation: A guide on how to record percentiles and interpret linear versus non-linear patterns in statistical visualizations.