1. Lecture 1 Sections 1.1 – 1.2 Objectives:
Populations, Samples and Processes
Visual Display for Univariate Data
Numerical Variables
Stem-and-Leaf Displays
Dotplots
Histograms
Categorical Variables
Bar Chart
Pie Chart
Introduction to R

2. Branches of Statistics
Descriptive Statistics
Exploratory Data Analysis (EDA)
Chapters 1 – 3
Used to summarize and describe important features in
the data, either graphically or numerically.
Inferential Statistics
Involves techniques for generalizing from a sample to a
population.
Chapters 7 – 8.

3. Population vs. Sample
Population: The entire group of individuals in which we are interested in but can’t usually assess directly.
E.g. all individuals who received a B.S in engineering in 2011.
Sample: The part of the population we actually examine and for which we do have data.
The sample is selected in some prescribed manner.
Population
Sample

4. Variables
We are usually interested only in certain characteristics of the objects in a population, e.g. the age of an engineering graduate, the gender of a graduate.
A characteristic may be categorical – e.g. gender - or it may be numerical – e.g. age.
A variable is any characteristic whose value may change from one object to another in the population. The value varies from object to object.
We will use lowercase letters to denote variable.
Example: x = age of a graduating engineer; y = braking distance of an automobile under specified conditions.

5. Discrete or Continuous
A variable is discrete if its set of possible values is either finite or can be listed in an infinite sequence.
A variable is continuous if its possible values consist of an entire interval on the number line.
e.g. x takes values 0,1,2,3,….
e.g. x is the pH of a chemical substance. x can take values like 7.0, 7.03, etc

6. Univariate vs. Multivariate
A univariate data set is when observations are made on a single variable.
E.g. type of transmission
A bivariate data set is when observations are made on two variables
E.g. (height, weight) pair for each basketball player.
A multivariate data set is when observations are made on more than two (multiple) variables

7. Example 1.1 (pg. 4)
The tragedy that befell the space shuttle Challenger and its astronauts in 1986 led to a number of studies to investigate the reasons for mission failure. Attention quickly focused on the behavior of the rocket engine’s O-rings. Here is data consisting of observations on x=O-ring Temperature (oF) for each test firing or actual launch of the shuttle rocket engine (Presidential Commission on the Space Shuttle Challenger Accident, Vol. 1, 1986: ).
Without any organization, it is very difficult to get a sense of what a typical or representative temperature might be, whether the values are highly concentrated about a typical value or quite spread out, whether there are any gaps in the data, what percentage of the values are in the 60s, and so on.

8. How to examine a distribution?
The distribution of a variable tells us what values the variable takes and how often it takes these values.
Almost always plot data as preliminary analysis
2. Look for the overall pattern
Shape
Location
Spread
3. Look for the striking deviation from overall pattern
Outlier

9. Stem-and-Leaf Plot How to make a stemplot:
Separate each observation into a stem, consisting of all but the final (rightmost) digit, and a leaf, which is that remaining final digit. Stems may have as many digits as needed, but each leaf contains only a single digit.
Write the stems in a vertical column with the smallest value at the top, and draw a vertical line at the right of this column.
Write each leaf in the row to the right of its stem, in increasing order out from the stem.
Stem 3 4 5 6 7 8
Leaf 1
059
23788

10. Histogram
The range of values that a variable can take is divided into equal size intervals.
The histogram shows the number of individual data points that fall in each interval.
Histogram Shapes
Unimodal, bimodal or multimodal
Symmetric, positively skewed or negatively skewed

12. Categorical Data
Because the variable is categorical, the data in the graph can be ordered any way we want (alphabetical, by increasing value, by year, by personal preference, etc.)
Bar graphs Each category is represented by a bar.
A Pareto diagram is a bar chart
from a quality control study
Pie charts The slices must represent the parts of one whole.

13. Some examples in R Example 1 Space Shuttle Challenger Accident Data
Stem-and-Leaf Graph: x=c(84,49,61,40,83,67,45,66,70,69,80,58,68,60,67,72,73,70,57,63,70,78,52,67,53,67,75,61,70,81,76,79,75,76,58,31) #temperature data
length(x) #the sample size
stem(x) #stem-and-leaf plot
Histogram:
hist(x,main="histogram of Temperature",xlab="Temperature") #histogram

14. Example 2
In the manufacture of printed circuit boards, finished boards are subjected to a final inspection before they are shipped to customers. Here is data on the type of defect for each board rejected at final inspection during a particular time period.
Type of defect Frequency
Low copper plating 112
Poor electroless coverage 35
Lamination problems 10
Plating separation 8
Etching problems 5
Miscellaneous
defect=c("Low copper plating","Poor electroless coverage","Lamination problems","Plating separation","Etching problems","Miscellaneaous") #type of defect
frequency=c(112,35,10,8,5,12) #frequency
Bar Graph: barplot(frequency,names.arg=defect) #barplot
Pie Chart: pie(frequency,labels=defect) #pie chart