Math Tech IIII, Jan 21
Fundamental Terms and Definitions I
Book Sections: 1.1
Essential Questions: What are the building blocks of Statistics, what do
I call them, and what do they mean? What are the branches of
statistics?
Standards: DA-4.1, DA-4.2, DA-4.3
Statistics
As a Branch of Mathematics
Statistics – The science of collecting, organizing,
analyzing, and interpreting data in order to make
decisions.
Key Words in Statistics
The Branches of Statistics
• Descriptive Statistics – Statistics that involve the
organization, summarization, and display of data.
 This is a set of methods to describe data that has been
collected.
• Inferential Statistics – Statistics that involve using a
sample to draw conclusions about a population. A
basic tool of inferential statistics is probability.
 This is a set of methods used to make a generalization,
estimate, prediction or decision.
Statistics Relationships
Statistics
A Mathematical Science
Descriptive
Statistics
Inferential
Statistics
The Simple Life Differences
Between The Branches of Statistics
• Descriptive Statistics – The facts or a computation
based on the facts
• Inferential Statistics – Making a prediction or drawing
a conclusion beyond the facts
Examples
Descriptive
• Of 350 randomly selected people in the town of Luserna,
Italy, 280 people had the last name Nicolussi.
• An example of descriptive statistics is the following
statement : "80% of these people have the last name
Nicolussi."
Examples
Inferential
• Of 350 randomly selected people in the town of Luserna,
Italy, 280 people had the last name Nicolussi.
• An example of inferential statistics is the following
statement : "80% of all people living in Italy have the last
name Nicolussi."
Why?
We have no information about all people living in Italy, just about
the 350 living in Luserna. We have taken that information and
generalized it to talk about all people living in Italy. The easiest
way to tell that this statement is not descriptive is by trying to
verify it based upon the information provided.
Examples
Descriptive or Inferential?
A large sample of 48 year old men was studied for 18 years.
Approximately 70% of single men and 90% of married men
was alive at age 65.
In a sample of Wall Street analysts, 44% incorrectly
forecasted high-tech earnings last year.
Examples
Descriptive or Inferential?
A large sample of 48 year old men was studied for 18 years.
Approximately 70% of single men and 90% of married men
was alive at age 65.
In a sample of Wall Street analysts, 44% incorrectly
forecasted high-tech earnings last year.
Examples
Descriptive or Inferential?
A large sample of 48 year old men was studied for 18 years.
Approximately 70% of single men and 90% of married men
was alive at age 65.
In a sample of Wall Street analysts, 44% incorrectly
forecasted high-tech earnings last year.
Common Manifestations
Descriptive or Inferential?
The most common use of descriptive statistics is a statistical
graph or visual representation.
The most common use of inferential statistics is a prediction.
Examples
New Math Symbol
What Does it Mean?
n
 xi
i 1
or
x
Sigma:  is a mathematical notation for
summation, or adding some numbers. This
notation simply means to add up all the values that
x could take on.
Example
If x is all values of the set {1, 2, 3, 4, 5} then
x
= 1 + 2 + 3 + 4 + 5 = 15
Examples
Calculator Data Input & List
Computations
Examples
2, 9, 5, 6, 1, 8, 4, 7, 3, 0
152, 271, 112, 149, 212, 161, 125, 222
Classwork: CW 1/21/15, 1-5
Homework – None