homework review my last name starts with a letter somewhere between a. a – d b. e – l c. m – r...
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Homework review
My last name starts with a letter somewhere between
A. A – DB. E – LC. M – RD. S – Z
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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.
http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man
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
What’s the largest possible
deviation? What’s the ‘typical’ or standard deviation?
Standard Deviation = 0.31
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)
What’s the largest possible
deviation?
1240 – 1700 = -460
2110 – 1700 = 410
Mean = 2.5 kidsRange = 1 - 8
What’s the ‘typical’ or standard deviation?
Standard Deviation = 1.7
Number of kids in familyWe sampled 100 families
(counted number of kids)
What’s the largest possible
deviation?
1 - 2.5= -1.5
8 – 2.5= 5.5
Mean = 80Range = 55 - 100
What’s the ‘typical’ or standard deviation?
Standard Deviation = 10
Number correct on examWe tested 100 students
(counted number of correct on 100 point test)
What’s the largest possible
deviation?
100 - 80 = 20
55 - 80= -25
Let’s try one
Standard Deviation = 27
Monthly electric bills for 50 apartments(amount of dollars charged for the
month)
150 – 213 = - 63
150 – 97 = 53
Mean = $150Range = 97 - 213
What’s the largest possible
deviation?
The best estimate of the population standard deviation isa. $150 b. $27c. $53d. $63
Let’s try one
Standard Deviation = 0.044
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
What’s the largest possible
deviation?2 – 1.894 = 0.106 2 – 2.109 = -0.109
Let’s try one
Standard Deviation = 10
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
What’s the largest possible
deviation?70 - 80
= 20
25 - 50= - 25
Let’s try one
Standard Deviation = 10
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
Standard Deviation = 10
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
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 …
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?
Heights of elementary students
Heights of 3rd graders
Other examples?
Variability and means
38 40 44 48 52 56 58
40 44 48 52 56
Remember, there is an implied axis
measuring frequencyf
f
Variability and means
What might this be an example of?
What might the standard deviation be?
Other examples?
0 4 8 12 16
0 4 8 12 16
Hours of homework – (kids K – 12)
Hours of homework – (7 grade)
Variability and means
What might this be an example of?
What might the standard deviation be?
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)
Variability and means
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
Variability and means
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)
Variability and means
Distributions different mean same variability
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)
Variability and means
Distributions different mean same variability
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)
Variability and means
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