Homework review My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Please click in Set your clicker to channel 41.

Homework review

My last name starts with a letter somewhere between

A. A – DB. E – LC. M – RD. S – Z

Please click in

Set your clicker to

channel 41

Introduction to Statistics for the Social Sciences

SBS200, COMM200, GEOG200, PA200, POL200, SOC200Lecture Section 001, Fall, 2011

Room 201 Physics-Atmospheric Sciences (PAS)10:00 - 10:50 Mondays & Wednesdays + Lab Session

http://www.youtube.com/watch?v=oSQJP40PcGI

By the end of lecture today 10/3/11

Use this as your study guide

Measures of variabilityStandard deviation and VarianceEstimating standard deviation

Exploring relationship between mean and variabilityEmpirical, classical and subjective approaches

Probability of an eventComplement of an event; Union of two events

Intersection of two events; Mutually exclusive eventsCollectively exhaustive events

Conditional probability

Please double check – All cell phones other electronic

devices are turned off and stowed away

Homework due - (October 5rd)

On class website: please print and complete homework worksheet #7

Please read:Chapters 5 - 9 in Lind book& Chapters 10, 11, 12 & 14 in Plous book: Lind

Chapter 5: Survey of Probability ConceptsChapter 6: Discrete Probability DistributionsChapter 7: Continuous Probability DistributionsChapter 8: Sampling Methods and CLTChapter 9: Estimation and Confidence Interval

PlousChapter 10: The Representativeness HeuristicChapter 11: The Availability HeuristicChapter 12: Probability and RiskChapter 14: The Perception of Randomness

Approach Example

Empirical There is a 2 percent chance of twins in a randomly-chosen birth.

Classical There is a 50 % probability of heads on a coin flip.

Subjective There is a 75 % chance that England will adopt the Euro currency by 2010.

Two mutually exclusive characteristics: if the occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic

Two events are mutually exclusive if they cannot occur at the same time (i.e. they have no outcomes in common).

Two propositions that logically cannot both be true.

http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

WarrantyNo

Warranty For example, a car repair is either covered by the

warranty (A) or not (B).


Events are collectively exhaustive if their union isthe entire sample space S.

Two mutually exclusive, collectively exhaustive events are dichotomous (or binary) events.

For example, a car repair is either covered by the

warranty (A) or not (B).

WarrantyNo

Warranty

Collectively Exhaustive Events

Satirical take on being “mutually exclusive”

Recently a public figure in the heat of the moment inadvertently made a statement that reflected extreme stereotyping that many would find highly offensive. It is within this context that comical satirists have used the concept of being “mutually exclusive” to have fun with the statement.


Transcript:Speaker 1: “He’s an Arab”

Speaker 2: “No ma’am, no ma’am. He’s a decent, family man, citizen…”

ArabDecent ,

family man

WarrantyNo

Warranty


Let’s estimate some standard deviation values

Standard deviation is a ‘spread’ score

We’re estimating the typical distance score(distance of each score from the mean)

Movie Packages We sampled 100 movie theaters

(Two tickets, large popcorn and 2 drinks)

Movie Packages We sampled 100 movie theaters

(Two tickets, large popcorn and 2 drinks)

Mean = $37Range = $27 - $47

What’s the largest possible

deviation? What’s the ‘typical’ or standard deviation?

Standard Deviation = 4.3

$47 – $37 = $10$27 – $37 = -$10

Waiting time for service at bankWe sampled 100 banks

(From time entering line to time reaching teller)

Mean = 3 minutesRange = 2.2- 3.6


deviation? What’s the ‘typical’ or standard deviation?


3.6 – 3.0= .62.2 – 3.0= -.8

Mean = 1700 poundsRange = 1240 – 2110

What’s the ‘typical’ or standard deviation?

Standard Deviation = 200

Pounds of pressure to break casing on an insulator

We sampled 100 insulators(applied pressure until the

insulator broke)


deviation?

1240 – 1700 = -460

2110 – 1700 = 410

Mean = 2.5 kidsRange = 1 - 8



Number of kids in familyWe sampled 100 families

(counted number of kids)


deviation?

1 - 2.5= -1.5

8 – 2.5= 5.5

Mean = 80Range = 55 - 100



Number correct on examWe tested 100 students

(counted number of correct on 100 point test)


deviation?

100 - 80 = 20

55 - 80= -25

Let’s try one


Monthly electric bills for 50 apartments(amount of dollars charged for the

month)

150 – 213 = - 63

150 – 97 = 53

Mean = $150Range = 97 - 213


deviation?

The best estimate of the population standard deviation isa. $150 b. $27c. $53d. $63

Let’s try one


Amount of soda in 2-liter containers(measured amount of soda in 2-liter

bottles)

The best estimate of the population standard deviation isa. 0.106b. 0.109c. 0.044d. 2.0

Mean = 2.0Range = 1.894 – 2.109


deviation?2 – 1.894 = 0.106 2 – 2.109 = -0.109

Let’s try one


Scores on an Art History exam(measured number correct out of 100)

The best estimate of the population standard deviation isa. 50b. 25c. 10d. .5

Mean = 50Range = 25 - 70


deviation?70 - 80

= 20

25 - 50= - 25

Let’s try one


Amount of soda in 2-liter containers(measured amount of soda in 2-liter

bottles)

The best estimate of the population standard deviation isa. 50b. 25c. 10d. .5

Mean = 50Range = 25 - 70

One way to estimate standard

deviation*

σ≈ range / 6

45 / 6 = 7.5

*See page 142 in text

Mean = 50Range = 25 - 70


Number correct on examWe tested 100 students

(counted number of correct on 100 point test)

If score is within 2 standard deviations (z < 2)“not unusual score”

If score is beyond 2 standard deviations (z ≥ 2)“is unusual score”

If score is beyond 3 standard deviations (z ≥ 3)“is an outlier”

If score is beyond 4 standard deviations (z ≥ 4)“is an extreme outlier”

Variability and means


38 40 44 48 52 56 58

40 44 48 52 56

What might this be an example of?

What might the standard deviation be?

The variability is different….

The mean is the same …


38 40 44 48 52 56 58

40 44 48 52 56



Heights of elementary students

Heights of 3rd graders

Other examples?


38 40 44 48 52 56 58

40 44 48 52 56

Remember, there is an implied axis

measuring frequencyf

f




Other examples?

0 4 8 12 16

0 4 8 12 16

Hours of homework – (kids K – 12)

Hours of homework – (7 grade)




Other examples?

40 50 60 70 80 90 100Score on driving test

Driving ability – (35 year olds)

40 50 60 70 80 90 100 Score on driving test

Driving ability – (16 - 90)


Distributions same mean different variability

Final exam scores “C” students versus whole class

Birth weight within a typical family versus within the whole community

Running speed 30 year olds vs. 20 – 40 year olds

Number of violent crimes Milwaukee vs. whole Midwest

Social distance (personal space) California vs international community


Distributions different mean same variability

Performance on a final exam Before versus after taking the class

40 50 60 70 80 90 100 Score on final (before taking class)

40 50 60 70 80 90 100 Score on final (before taking class)



62 64 66 68 70 72 74 76Inches in height (women)

Height of men versus women

62 64 66 68 70 72 74 76Inches in height (men)



2 4 6 8 10 12 14 16Number of errors (not on phone)

Driving ability Talking on a cell phone or not

2 4 6 8 10 12 14 16Number of errors (on phone)


Comparing distributions different mean same variability

Performance on a final exam Before versus after taking the class

Height of men versus women

Driving ability Talking on a cell phone or not

. Writing AssignmentComparing distributions (mean and variability)

Think of examples for these three situations• same mean but different variability • same variability but different means• same mean and same variability (different groups)• estimate standard deviation • calculate variance• for each curve find the raw score for the z’s given on

worksheet

Homework review My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Please click in Set your clicker to channel 41.

Documents

mean slide

warranty slide

exclusive events

largest possible deviation

homework review slide

binary events

perception of randomness

events intersection