1. What is Statistics?
Statistics is the science of:
 Collecting data
 Analyzing data
 Drawing conclusions from data

2. Statistics include numerical facts and
figures such as:
 The largest earthquake measured 9.2 on the Richter
scale.
 Men are at least 10 times more likely than women to
commit murder.
 One in every 8 South Africans is HIV positive.
 By the year 2020, there will be 15 people aged 65
and over for every new baby born.

3. Why should we study statistics?
 We want to make sense of the world.
 We don’t want to be lied to.
 We want to be able to spot trends that help us make
good decisions.

4. 4 Main Themes:
I. Exploring data (compare graphs and numbers)
II. Sampling & Experimentation (collect data)
III. Anticipating Patterns (Probability and Simulation)
IV. Statistical Inference (Make conclusions)

5.  Individuals are the objects described by a set of data.
 Variable is any characteristic of an individual.
EXAMPLE: An AP Statistics class list contains information
about the students enrolled. The students enrolled are the
individuals, and for each individual, there are variables
such as student number, gender and home phone number.

6. Check For Understanding
 You want to compare the “size of several AP statistics
textbooks. Give at least three possible numerical variables
that describe the “size” of a book. In what units would you
measure each variable?

7. Possible Answers (units)
 Number of pages (pages)
 Number of words (words)
 Volume (cubic inches, cubic centimeters)
 Height and/or width (pounds, ounces)
 Number of chapters (chapters)
 Weight (pounds, ounces)

8. Types of variables:
 A categorical variable places an individual into one of
several groups or categories.
 Examples: gender, letter grade, zip code
 A quantitative variable takes numerical values for which
arithmetic operations such as adding and averaging make
sense.
 Examples: scores on a test, age, GPA

9. Check for Understanding
 Data from a medical study contain values of many variables
for each of the people who were the subjects of the study.
Which of the following variables are categorical and which are
quantitative?
(a) gender (female or male)
(b) Age (years)
(c) Race (Asian, black, white,or other)
(d) Smoker (yes or no)
(e) Systolic blood pressure (millimeters of mercury)
(f) Level of calcium in the blood (micrograms per milliliter)

10. Answers
(a) categorical
(b) quantitative
(c) categorical
(d) categorical
(e) quantitative
(f) quantitative

11. The distribution of a variable is a list (chart, picture,
etc.) that tells us what values the variable takes and
how often it takes these values.
Most variables take on values that vary. Sometimes
those values are clustered close together, and other
times they are spread far apart. When we look at
how those values vary, we are looking at the
distribution of the variable.

12. Important features of a distribution:
Shape
 Is the distribution symmetric or skewed?
Outliers
 Are there individual observation that falls outside the overall
pattern of the graph?
Center
 Is there a typical or most common value of the variable? Is
there a mode? Bimodal?
Spread
 What is the range of possible values? How wide is the
distribution?

13. Check For Understanding
The histogram below shows the
distribution of total returns for all
1528 stocks listed on the New
York State Exchange in one year.
(a) Describe the overall shape of the
distribution of total returns.
(b) What is the approximate center
of this distribution? (For now,
take the center to be the value
with roughly half the stocks
having lower returns and half
having higher returns.)
(c) Approximately what were the
smallest and largest total
returns? (This describes the
spread of the distribution)

14. Answers
(a) Roughly symmetric, though it might be viewed as SLIGHTLY
skewed to the right.
(b) About 15%. (39% of the stocks had a total return less than
10%, while 60% had a return less than 20%. This places the
center of the distribution somewhere between 10% and
20%.)
(c) The smallest return was between -70% and -60%, while the
largest was between 100% and 110%.

15. When analyzing data,
ask the following:
 Who are the individuals being described?
 What are the variables?
 Why were the data gathered?
 When, where, how, and by whom were the data
produced?

16. Check For Understanding
In October 2005 Discover published an article on the colonies of ants. They
reported some basic information about many species of ants and the results of
some discoveries found by myrmecologist Walter Tschinkel of the University of
Florida. Information included the scientific name of the ant species, the
geographic location, the depth of the nest (in feet), the number of chambers in
the nest, and the number of ants in the colony. The article documented how new
ant colonies begin, the ant-nest design, and how nests differ in shape, number,
size of chambers, and how they are connected, depending on the species. It
reported that nest designs include vertical, horizontal, or inclined tunnels for
movement and transport of food and ants.
Describe the W's, if the information is given. If the information is not given, state
that it is not specified.
 Who:
 What:
 When:
 Where:
 How:
 Why:

17. Answers
 Who: Colonies of ants. "Many species of ants," but no
indication of exactly how many.
 What: scientific name, geographic location, average nest
depth, average number of chambers, average colony size,
how new ant colonies begin, the ant-nest design, and how
nests differ in architecture.
 When: October 2005
 Where: not specified
 How: The results of some discoveries found by myrmecologist
Walter Tschinkel of the University of Florida
 Why: Information of interest to readers of the magazine