chapter 1

Quote of the Day

Oh, people can come up with statistics to prove anything. 14% of people know that. ---Homer Simpson

What are Statistics?

Chapter 1:The Nature of Probability and Statistics

Section 1:Descriptive and Inferential

Statistics

Stats in Daily Life Of the people in the US, 14% said they

feel happiest in June, and 14% said they feel happiest in December.

The average in-state college tuition and fees for 4-year pubic college is $5,836.

Every day in the US about 120 golfers claim that they made a hole-in-one.

4 out of 5 doctors leaves one doctor.- Chevy Chase

What is Statistics? The science of conducting studies to

collect, organize, summarize, analyze and draw conclusions from data.

What is Data?

The values that the variables can assume.

A collection of values forms a Data Set Each Value in the data set is called:

Data Value or Datum

What is a variable?

A characteristic or attribute that can assume different values.

Types of Statistics

1. Descriptive Statistics Consists of the collection, organization,

summarization, and presentation of data Ex: Government Census

Taken every ten years Describes average income, family size, etc..

What does this mean? Basically used to describe a situation.

Types of Statistics

2. Inferential Statistics Consists of generalizing from samples to

populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions.

Ex: Winning the lottery 1 in a million

What does this mean ? Used to predict the outcome of an event.

What is the difference between a Population and a Sample?

Population- consists of all subjects that are being studied.

Sample- is a group selected from a population.

Population Sample

Assignment

Page 26 #’s 1-6

Section 2: Types of Variables

Qualitative Variables: Variables that can be placed into

distinct categories, according to some characteristic or attribute.

Ex: Gender, Eye color, Geographic Location

2 Types of Variables

Quantitative Variables: Variables that are numerical and can

be ordered or ranked. Ex: Age, height, weight, body temp Classified by two groups

Discrete Variables Continuous Variables

Practice

Page 26 #8

Discrete Variables

Assume values that can be counted

Assigned numbers such as 0,1,2,3,…

Ex: # of children # of students

Continuous Variables Can assume an infinite number of

values between any two specific values.

Obtained by measuring Often include fractions and decimals. Ex:

Temperature Time Length

Practice

Page 27 #9

Measurement Scale

Used to categorize, count, or measure variables.

Types: Nominal Ordinal Interval Ratio

Nominal Level of Measurement

Classifies data into mutually exclusive, exhausting categories in which no order or ranking can be imposed on the data.

Ex: Male/Female Single/Married/Divorced/Widowed/Separated Democratic/Republican

Ordinal Level of Measurement Classifies data into categories that

can be ranked; however, precise differences between the ranks do not exist.

Ex: Letter Grades (A, B, C, D, F) 1st, 2nd, 3rd, etc Small, Medium, Large Freshman, Sophomores, Juniors, Seniors

Interval Level of Measurement Ranks data, and precise differences

between units of measures do exist: however, there is no meaningful zero.

Ex: Temperature: 72°F and 73°F, difference

of 1°F, but 0°F does not mean no heat present

IQ: 109 and 110, difference of 1 point, but 0 does not mean there is no intelligence.

Ratio Level of Measurement Possesses all the characteristics of

interval measurements, and there exists a true zero.

In addition, true ratios exists when the same variables is measured on two different members of the population.

Ex: Salary Time Age

Practice

Page 26 #7

Section 3: Data Collection and Sampling Techniques.

Types: Random Systematic Stratified Cluster

Random Sampling

Selection based on chance or random numbers.

Procedure: Assign number to each subject in

population Select numbers at random from “hat”

Random Sampling

1 2 3 4 5 6 7

8 9 10

11 12 13 14

15 16 17 18 19 20 21

Systematic Sampling

Procedure: Number each subject in population Select every kth subject

Example: Population: 100 Sample: 10 Kth term: 100/10=10 1, 11, 21, 31, 41, 51, 61, 71, 81, 91

Systematic SamplingPopulation: 21 Sample: 721/7=3: kth term is 3.

1 2 3 4 5 6 7

8 9 10

11 12 13 14

15 16 17 18 19 20 21

Stratified Sampling

Procedures: Population divided into groups called:

Strata Groups have common characteristic

needed for study. Samples randomly selected from each

strata

Stratified Sampling

Cluster Sampling

Population is divided into groups called: Clusters

Select some clusters Survey every member of the

cluster for sample

Used with large populations

Cluster Sampling

Other sampling methods

Convenience sampling Use subjects that are convent Ex: asking people as they enter the

mall Sequential sampling Double sampling Multistage sampling

Convenience Sampling

Do you want to take a survey?

Practice

Page 27 #12

Section 4: 2 Types of Studies

Observational Study Researchers merely observe what is

happening or what has happened in the past

Try to draw conclusions based on these observations.

Ex: studying creatures in the wild “Meerkat Manor”

Experimental study Researchers manipulate one of the

variables Tries to determine how to the

manipulation influences other variables.

Ex: New medication and placebos

Section 4: 2 Types of Studies

Practice

Page 27-28 #17

Statistical Studies include…. Independent variables

In an experimental study is the one that is being manipulated by the researcher.

Also called: Explanatory variable

Dependent variables Resultant variable Also called: Outcome variable

Misuses of Statistics Suspect Samples

Too small Convenience Volunteers

Changing the subject Increase of 3% Increase of $600,000

Detached Statistics- no comparison “Works 5 times faster” “1/3 fewer calories”

Implied Connection “Eating fish may help you achieve

better in school”

Misuses of Statistics

Misleading Graphs- Chapter 2

Faulty Survey Questions “Do you feel there should be a 4 day

school week?” “Do you feel there should be a 4 day

school week from 4 am to midnight?”

Misuses of Statistics

Section 1-6: Computers and Calculators

Computer and Calculators GOOD

End of Chapter 1