Chapter 1 Overview and Descriptive Statistics Note that these are textbook chapters, although Lecture Notes may be referenced. 1.1 - Populations, Samples and Processes 1.2 - Pictorial and Tabular Methods in Descriptive Statistics 1.3 - Measures of Location 1.4 - Measures of Variability

PROBABILITY IN A NUTSHELL

“Probability Theory” makes theoretical predictions of the occurrence of events where randomness is present, via known mathematical models.

“Probability Theory” makes theoretical predictions of the occurrence of events where randomness is present, via known mathematical models.

“Probability Theory” makes theoretical predictions of the occurrence of events where randomness is present, via known mathematical models.

POPULATION (of “units”) uniform X = “Random Variable” symmetric unimodal “REAL WORLD” SYSTEM skew (positive) PROBABILTY MODEL YES Model has to be tweaked. THEORY EXPERIMENT Is there a significant difference? Random Sample Model Predictions STATISTICS How do we test them? NO Model may be adequate / useful.

POPULATION (of “units”) uniform “Arbitrarily large” or infinite collection of units (rocks, toasters, people, districts,…) X = “Random Variable” symmetric unimodal “REAL WORLD” SYSTEM A numerical value assigned to each unit of the population skew (positive) PROBABILTY MODEL Temp Mass Foot length Shoe size # children TV channel Alphabet Zip Code Shirt color Coin toss Pregnant? Quantitative (Measurements) (A = 01,…, Z = 26) Qualitative (Categories) (Blue = 1, White = 2…) (Heads = 1, Tails = 0) (Yes = 1, No = 0)

POPULATION (of “units”) uniform skew (positive) symmetric unimodal “Arbitrarily large” or infinite collection of units (rocks, toasters, people, districts,…) X = “Random Variable” “REAL WORLD” SYSTEM A numerical value assigned to each unit of the population PROBABILTY MODEL Temp Mass Foot length Shoe size # children TV channel Alphabet Zip Code Shirt color Coin toss Pregnant? Continuous Quantitative (Measurements) Discrete Ordinal (A = 01,…, Z = 26) Qualitative (Categories) (Blue = 1, White = 2…) Nominal (Heads = 1, Tails = 0) Binary (Yes = 1, No = 0)

POPULATION (of “units”) uniform skew (positive) symmetric unimodal “Arbitrarily large” or infinite collection of units (rocks, toasters, people, districts,…) X = “Random Variable” “REAL WORLD” SYSTEM A numerical value assigned to each unit of the population PROBABILTY MODEL Temp Mass Foot length Shoe size # children Coin toss Pregnant? Continuous Continuous Quantitative (Measurements) Discrete Discrete Qualitative (Categories) (Heads = 1, Tails = 0) Binary (Yes = 1, No = 0)

POPULATION (of “units”) uniform skew (positive) symmetric unimodal “Arbitrarily large” or infinite collection of units (rocks, toasters, people, districts,…) X = “Random Variable” “REAL WORLD” SYSTEM A numerical value assigned to each unit of the population PROBABILTY MODEL Temp Mass Foot length Shoe size # children Continuous Continuous Quantitative (Measurements) Discrete Discrete “probability density function” “histogram” Qualitative (Categories) “probability mass function”

What is “random variation” in the distribution of a population? Examples: Toasting time, Temperature settings, etc. of a population of toasters… POPULATION 1: Little to no variation (e.g., product manufacturing) In engineering situations such as this, we try to maintain “quality control”… i.e., “tight tolerance levels,” high precision, low variability. O O O O O But what about a population of, say, people?

What is “random variation” in the distribution of a population? Example: Body Temperature (F) POPULATION 1: Little to no variation (e.g., clones) Density Most individual values ≈ population mean value Very little variation about the mean! 98.6 F

What is “random variation” in the distribution of a population? Example: Body Temperature (F) Examples: Gender, Race, Age, Height, Annual Income,… POPULATION 2: Much variation (more common) Density Much more variation about the mean!