1. 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

3. PROBABILITY IN A NUTSHELL

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

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

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

7. 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.

8. 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)

9. 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)

10. 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)

11. 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”

12. 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?

13. 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

14. 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!