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Lecturer’s desk

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Screen

Cabinet

Cabinet

Lecturer’s desk

Table

Computer Storage Cabinet

Row A

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Row C

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Row D

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Row E

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Row F

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Row G

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Row H

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Row I

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Row J

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Row K

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Row L

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INTEGRATED LEARNING CENTER

ILC 120

9

8

10

12

11

broken

desk

Please click in

My last name starts with a

letter somewhere between

A. A – D

B. E – L

C. M – R

D. S – Z

Remember to hold onto homework until we have a chance to cover it

Introduction to Statistics for the Social SciencesSBS200, COMM200, GEOG200, PA200, POL200, SOC200Lecture Section 001, Spring, 2012Room 120 Integrated Learning Center (ILC)9:00 - 9:50 Mondays, Wednesdays & Fridays+ Lab Session.

Welcome

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

Use this as your

study guide

- Objectives of research in business
- Characteristics of a distribution
- Central Tendency
- Dispersion
- Shape

- What are the three primary types of “measures of central
- tendency”?
- Mean
- Median
- Mode

- Measures of variability
- Range, Standard deviation and Variance
- Memorizing the four definitional formulae

Schedule of readings

Before next exam (February 10th):

Please read chapters 1 - 4 &

Appendix D, E & F online

Please read Chapters 1, 5, 6 and 13 in Plous

Chapter 1: Selective Perception

Chapter 5: Plasticity

Chapter 6: Effects of Question Wording and Framing

Chapter 13: Anchoring and Adjustment

Homework Assignment #6

due Monday (February 6th)

Please double check – Allcell phones other electronic devices are turned off and stowed away

The normal curve

Challenge yourself as we work through characteristics of distributions to try to categorize each concept as a measure of

1) central tendency

2) dispersion or 3) shape

Mean, Median,

Mode, Trimmed Mean

Standard deviation,

Variance, Range

Mean Absolute Deviation

Skewed right, skewed left

unimodal, bimodal, symmetric

An example of a normal distribution

An example of a normal distribution

An example of a normal distribution

An example of a normal distribution

An example of a normal distribution

Normal distribution

In all distributions:

mode = tallest point

median = middle score

mean = balance point

In a normal distribution:

mode = mean = median

Positively skewed distribution

In all distributions:

mode = tallest point

median = middle score

mean = balance point

In a positively skewed distribution:

mode < median < mean

Note: mean is most affected by outliers or skewed distributions

Negatively skewed distribution

In all distributions:

mode = tallest point

median = middle score

mean = balance point

In a negatively skewed distribution:

mean < median < mode

Note: mean is most affected by outliers or skewed distributions

Mode: The value of the most frequent observation

Bimodal distribution: Distribution with two most

frequent observations (2 peaks)

Example: Ian coaches two boys baseball teams. One team is made up of 10-year-olds and the other is made up of 16-year-olds. When he measured the height of all of his players he found a bimodal distribution

The normal curve

Mean, Median,

Mode, Trimmed Mean

Standard deviation,

Variance, Range

Mean Absolute Deviation

Skewed right, skewed left

unimodal, bimodal, symmetric

5’

7’

6’

6’6”

5’6”

5’

7’

6’

6’6”

5’6”

5’

7’

6’

6’6”

5’6”

Variability

The larger the variability

the wider the curve

tends to be

The smaller the variability

the narrower the curve

tends to be

5’

7’

6’

6’6”

5’6”

5’

7’

6’

6’6”

5’6”

5’

7’

6’

6’6”

5’6”

Some distributions are more variable than others

A

Range: The difference between

the largest and smallest

observations

B

Range for distribution A?

Range for distribution B?

Range for distribution C?

C

Fun fact:

Mean is 72

Wildcats Baseball team:

Tallest player = 76” (same as 6’4”)

Shortest player = 68” (same as 5’8”)

Range:

The difference

between the largest

and smallest scores

76” – 68” = 8”

Range is 8” (76” – 68”)

xmax - xmin = Range

Please note:

No reference is made to numbers between the min and max

Fun fact:

Mean is 78

Wildcats Basketball team:

Tallest player = 83” (same as 6’11”)

Shortest player = 70” (same as 5’10”)

Range is 13” (83” – 70”)

Range:

The difference

between the largest

and smallest scores

83” – 70” = 13”

xmax - xmin = Range

The normal curve

What might this be?

Some distributions are more

variable than others

Let’s say this is our distribution of heights of men on U of A baseball team

5’

7’

6’

6’6”

5’6”

5’

7’

6’

6’6”

5’6”

Mean is 6 feet tall

What might this be?

5’

7’

6’

6’6”

5’6”

5’

7’

6’

6’6”

5’6”

5’

7’

6’

6’6”

5’6”

5’

7’

6’

6’6”

5’6”

Variability

The larger the variability

the wider the curve

the larger the deviations

scores tend to be

The smaller the variability

the narrower the curve

the smaller the deviations

scores tend to be

Diallo is 6’0”

Diallo

5’8” 5’10” 6’0” 6’2” 6’4”

Let’s build it up again…U of A Baseball team

Diallo is 6’0”

Preston is 6’2”

Preston

5’8” 5’10” 6’0” 6’2” 6’4”

Let’s build it up again…U of A Baseball team

Diallo is 6’0”

Preston is 6’2”

Hunter

Mike is 5’8”

Mike

Hunter is 5’10”

5’8” 5’10” 6’0” 6’2” 6’4”

Let’s build it up again…U of A Baseball team

Diallo is 6’0”

Preston is 6’2”

David

Mike is 5’8”

Shea

Hunter is 5’10”

Shea is 6’4”

David is 6’ 0”

5’8” 5’10” 6’0” 6’2” 6’4”

Let’s build it up again…U of A Baseball team

Diallo is 6’0”

Preston is 6’2”

David

Mike is 5’8”

Shea

Hunter is 5’10”

Shea is 6’4”

David is 6’ 0”

5’8” 5’10” 6’0” 6’2” 6’4”

Let’s build it up again…U of A Baseball team

Diallo is 6’0”

Preston is 6’2”

Mike is 5’8”

Hunter is 5’10”

Shea is 6’4”

David is 6’ 0”

5’8” 5’10” 6’0” 6’2” 6’4”

Let’s build it up again…U of A Baseball team

5’8” 5’10” 6’0” 6’2” 6’4”

5’8” 5’10” 6’0” 6’2” 6’4”

Standard deviation: The average amount by which observations deviate on either side of their mean

Generally, (on average) how far away is each score from the mean?

Mean is 6’

Deviation scores

Diallo is 0”

Diallo is 6’0”

Diallo’s deviation score is 0

6’0” – 6’0” = 0

Diallo

5’8” 5’10” 6’0” 6’2” 6’4”

Deviation scores

Diallo is 0”

Let’s build it up again…U of A Baseball team

Preston is 2”

Diallo is 6’0”

Diallo’s deviation score is 0

Preston is 6’2”

Preston

Preston’s deviation score is 2”

6’2” – 6’0” = 2

5’8” 5’10” 6’0” 6’2” 6’4”

Deviation scores

Diallo is 0”

Let’s build it up again…U of A Baseball team

Preston is 2”

Mike is -4”

Hunter is -2

Diallo is 6’0”

Diallo’s deviation score is 0

Hunter

Preston is 6’2”

Preston’s deviation score is 2”

Mike

Mike is 5’8”

Mike’s deviation score is -4”

5’8” – 6’0” = -4

5’8” 5’10” 6’0” 6’2” 6’4”

Hunter is 5’10”

Hunter’s deviation score is -2”

5’10” – 6’0” = -2

Deviation scores

Diallo is 0”

Let’s build it up again…U of A Baseball team

Preston is 2”

Mike is -4”

Hunter is -2

Shea is 4

David is 0”

Diallo’s deviation score is 0

David

Preston’s deviation score is 2”

Mike’s deviation score is -4”

Shea

Hunter’s deviation score is -2”

Shea is 6’4”

Shea’s deviation score is 4”

5’8” 5’10” 6’0” 6’2” 6’4”

6’4” – 6’0” = 4

David is 6’ 0”

David’s deviation score is 0

6’ 0” – 6’0” = 0

Deviation scores

Diallo is 0”

Let’s build it up again…U of A Baseball team

Preston is 2”

Mike is -4”

Hunter is -2

Shea is 4

David is 0”

Diallo’s deviation score is 0

David

Preston’s deviation score is 2”

Mike’s deviation score is -4”

Shea

Hunter’s deviation score is -2”

Shea’s deviation score is 4”

David’s deviation score is 4”

5’8” 5’10” 6’0” 6’2” 6’4”

Deviation scores

Diallo is 0”

Let’s build it up again…U of A Baseball team

Preston is 2”

Mike is -4”

Hunter is -2

Shea is 4

David is 0”

5’8” 5’10” 6’0” 6’2” 6’4”

Deviation scores

Standard deviation: The average amount

by which observations deviate on either side

of their mean

Diallo is 0”

Preston is 2”

Mike is -4”

Hunter is -2

Shea is 4

David is 0”

5’8” 5’10” 6’0” 6’2” 6’4”

Deviation scores

Standard deviation: The average amount

by which observations deviate on either side

of their mean

Diallo is 0”

Preston is 2”

Mike is -4”

Hunter is -2

Shea is 4

David is 0”

5’8” 5’10” 6’0” 6’2” 6’4”

Σ(x - x) = 0

Deviation scores

Standard deviation:

The average amount by which

observations deviate on either

side of their mean

Diallo is 0”

Preston is 2”

Mike is -4”

Hunter is -2

Shea is 4

David is 0”

Mike

Σ x - x = ?

Hunter

5’8” - 6’0” = - 4”

5’9” - 6’0” = - 3”

5’10’ - 6’0” = - 2”

5’11” - 6’0” = - 1”

6’0” - 6’0 = 0

6’1” - 6’0” = + 1”

6’2” - 6’0” = + 2”

6’3” - 6’0” = + 3”

6’4” - 6’0” = + 4”

Diallo

5’8” 5’10” 6’0” 6’2” 6’4”

How do we find the average deviation?

Preston

Σx / n = mean

Σ(x - µ) = 0

Σ(x - x)

Σ(x - x) = 0

Deviation scores

Standard deviation:

The average amount by which

observations deviate on either

side of their mean

Diallo is 0”

Preston is 2”

Mike is -4”

Hunter is -2

Shea is 4

How do we find the average deviation?

David is 0”

Square the deviations!!

(and later take square root)

Σx / n = mean

Σ x - x = ?

2

5’8” - 6’0” = - 4”

5’9” - 6’0” = - 3”

5’10’ - 6’0” = - 2”

5’11” - 6’0” = - 1”

6’0” - 6’0 = 0

6’1” - 6’0” = + 1”

6’2” - 6’0” = + 2”

6’3” - 6’0” = + 3”

6’4” - 6’0” = + 4”

2

Σ(x - µ)

How do we get rid of the negatives??!?

Big problem!!

Σ(x - µ) = 0

Standard deviation: The average amount by which observations

deviate on either side of their mean

Note this is for population standard deviation

Fun Fact:

Standard deviation squared = variance

Standard deviation: The average amount by which observations

deviate on either side of their mean

Note this is for sample

standard deviation

Fun Fact:

Standard deviation squared = variance

Standard deviation: The average amount by which observations

deviate on either side of their mean

These would be helpful to know by heart – please memorize

these formula

Thank you!

See you next time!!