Statistics Video Playlist

(1)

Statistics Chapter

(2)

Statistics

 Is the process of attempting to organize and

understand raw (unorganized) information.  Descriptive Statistics

 Goals

 Learn some terminology used in basic statistics.

 Understand the purpose of basic statistical measures.

 Learn how to compute and use basic statistical

(3)

(4)

(5)

Wisconsin Pay Data

(6)

Statistics in Graphical Form

(7)

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Statistics in Graphical Form

Frequency Distribution

Miles Driven 0 – 9

9 –18 18 – 27 27 – 36 36 – 45 45 – 54

Frequency 1 3 3 7 0 1

0.2 54 30 11

24 30 32 20

11 32 12 24

30 35 29

1-way distance driven from home to SWTC:

(9)

Statistical Tools

(10)

Statistics

 Is the process of attempting to organize and

understand raw (unorganized) information.  Descriptive Statistics

 Goals

 Learn some terminology used in basic statistics.

 Understand the purpose of basic statistical measures.

 Learn how to compute and use basic statistical

measures.

(11)

Definition

 A measure of central tendency is used to:

 Represent or describe an entire group of data with

a single number.

 Indicate the middle of a collection of data.

My Blueprint Reading Test Scores

82 76 75 90

71 72 80 83

(12)

3 types…

 Measures of Central Tendency 1. mean

2. median

(13)

Measures of Central

Tendency

0.2 55 30 11

24 30 32 20

11 32 12 23.5

30 35 29

Survey of 15 students:

1-way distance driven from home to SWTC:

(14)

Formula to compute the mean ( )

Sum* of the data

n

Note:

In statistics:

n = the quantity of data you are working with. Note:

In statistics:

n = the quantity of data you are working with.



(15)

0.2 55 30 11

24 30 32 20

11 32 12 23.5

30 35 29

Commuting Distance: mean

(

)

Sum of the data

n

374.7 15

Like any measure of central tendency, the mean is:

a single value that is

intended to represent the entire set of data.

an attempt to show the

middle of the data set.



(16)

Practice

Compute mean ()

 Practice Set 1 Compute the mean

(17)

The mean in practice…

 Carpenters earn an average annual wage of

$44,520…

mean mean

(18)

Practice – Compute the Mean

Royal Oakes Subdivision

Assessed home prices on eight homes:

$125,000 $135,000 $140,000 $110,000 $150,000 $380,000 $127,000 $148,000

What is the mean home value?Sum of the data

(19)

Median – middle of an

(20)

88 72 71 92 60 83 75

Median

Ordered set (lowest  highest)

(21)

Median

 If n is even…

88 72 71 92 60 83

Median = 77.5

(22)

Practice – Compute the

Median

Royal Oakes Subdivision

Assessed home prices on eight homes:

$125,000 $135,000 $140,000 $110,000 $150,000 $380,000 $127,000 $148,000

What is the median home value? $110,000 $125,000 $127,000 $135,000 $140,000 $148,000 $150,000 $380,000

Median = $137,500

(23)

0.2 55 30 11

24 30 32 20

11 32 12 23.5

30 35 29

mean = 25 miles

median = 29 miles

Median

0.2 11 11 12 20 24 24 29 30 30 30 32 32 35 5523.5

(24)

Practice

 Practice Set 2 – Compute the median

(25)

Mode – the most frequently

occurring.

Soft Drinks

(26)

0.2 55 30 11

24 30 32 20

11 32 12 23.5

30 35 29

mean = 25 miles

Mode

median = 29 miles

(27)

Practice

 Practice Set 3 – Compute the mode.

(28)

Review of Section 1

 Review all three measures of central

tendency

 Practice Set 4

(29)

Weighted Average

Average Price per Item

Number of Items

Purchased Price per Item ( Welding Gloves )

40 $4.85

10 $6.50

5 $6.75

80 $4.95

90 $5.05

Average Price = ?_$5.62 x = x = x = x = x =

$194.00 $65.00 $33.75 $396.00 $454.50 $1143.25 225 items

(30)

Weighted Average

Grade Point Average

Grade Grade as a

Number Number of

Credits A 5 A 2 C 3 B 3 D 1

Average Grade = ?2.8 avg.

x = x = x = x = x =

20 grade pts 8

6 9 1

44 gr. pts. 14 credits

= 3.14 GPA

(31)

Practice

 Assignment List

(32)

Statistics

Section 2

(33)

Introduction

Making decisions based on central tendency.

(34)

Mean (average) depth = 4.2 ft

(35)

(36)

Moral of the story…

 Even though knowing mean, median, and

(37)

Variability

Defined

 Variability refers to how different the data

values are from one another.

 In this group of numbers; 5, 5, 6, 6, 6, 6, 8

 The variability is very low because the numbers are very

similar in size.

 You can also say that this collection of numbers is very

(38)

Variability

Defined

 Variability refers to how different the data

values are from one another.

 In this group of numbers; 2, 13, 14, 29, 36, 60, 91

 The variability is higher because the numbers are not

similar in size.

 You can also say that this collection of numbers is not

(39)

Introduction to

Variability

Who is the better bowler?  Bowler A:

 Bowler B:

Mean Score = 132

(40)

Introduction to

Variability

Who is the more consistent bowler?  Bowler A:

 Bowler B:

Bowler A: Scores are “all over the road”. Bowler B: Scores are very similar.

128, 150, 103, 161, 117 141, 148, 151, 143, 149

Mean Score = 132

Mean Score = 146



?

Are the scores similar?

(41)

70 68 67 69 65

67 61 62 77 74

72 68 66 69 67

69 70 70 69 69

67 73 69 72 74

72 69 68 71 68

73 69 67 71 71

71 73 63 63 69

68 70 74 73 71

73 66 72 74 71

61 68 64 66 77

70 76 67 69 71

67 74 77 69 70

68 69 63 72 65

67 72 73 68 77

70 72 66 69

63 70 70 69 69

74 69 69 74 70

70 72 68 74 70

65 71 68 68 74

73 76 70 69 75

67 73 71 73 69

71 68 72 73 70

75 65 73 72 72

71 68 71 66 71

68 70 67 69 68

66 70 76 75 71

71 75 68 71 65

69 70 75 72 77

74 73 69 70 73

68 78 69 75 69

76 68 74 69 69

68 68 65 69 68

66 67 67 68 71

70 67 70

Steve Stricker 2009 PGA Data

Ben Crane 2009 PGA Data

Which golfer is more consistent?

(42)

Tools to Measure Variability

 Range

Range = Highest Number - Lowest Number

 A small range means the data values are all very similar.

 A large range means the data values are dissimilar.*

 Standard Deviation

 later…

Range = High – Low

Range = $5.329 – $2.509 Range = $2.82

(43)

Variability

Range

 Who is the more consistent welder based

on number of defective welds per week?

 Compute the range to decide.

 Welder A: 5, 2, 2, 1, 4, 4

 Range = 5 – 1 = 4

 Welder B: 8, 8, 6, 7, 7, 6

 Range = 8 – 6 = 2

Since the range is smaller for Welder B, he/she appears to be the more consistent welder…

(44)

Welding I Pay Data

 Median annual pay for 17

cities in the upper Midwest as of October 2013:

median = $33,495

If you are willing to relocate anywhere in the region how choosy do you have to be in terms of picking a city?

Compute the range to help answer this question: __________

Range = High – Low

$6,945

(45)

Practice

Range

 Practice Set 5, page 17 & 18

(46)

Variability

Range-drawbacks

 Which blueprint reading student has the least

variability in their test scores?

 Compute the range to decide.

 Student A (test scores): 95, 94, 93, 65, 92, 89

 Range = 95 – 65 = 30

 Student B (test scores): 80, 61, 88, 65, 70, 58

 Range = 88 – 58 = 30

outli er

(47)

Review

 Measures of Central Tendency

 mean  median  mode

 Measures of Variability

 range

 standard deviation

Test Scores

75, 78, 60, 82, 85, 70, 70

74.3

75 70

25

8.5

How “good” is this student?

How variable are the test scores ?

Are the scores similar to one another or are they more

(48)

Variability

Standard Deviation “Casual Definition”

 Standard Deviation - describes the average

"distance" a typical piece of data is from the middle of the data set.

 Student A: 80, 61, 88, 65, 70, 58

70.3 80

61 65

58 70 88

Ave. Distance = 9.1

(49)

Variability

Standard Deviation “Casual Definition”

 Standard Deviation - describes the average

"distance" a typical piece of data is from the middle of the data set.

 Student B: 77, 71, 66, 67, 68, 73

70.3 73 67 68

66 71 77

Ave. Distance = 3.3

(50)

Compute Standard Deviation

 Calculator

 Basic model (p. 21)  Scientific

 Computer

 Spreadsheet: Excel  Online

easycalculation.com

 App:



Stats Calculator

Free (Android)

(51)

Practice

Standard Deviation

(52)

Statistics

(53)

Data Set “shapes”

 Frequency Distributions allow you to “see”

the data you are working with:

Class Frequency

15-21 years old 1863

22-28 636 29-35 417 36-42 452 43-49 397 50-56 251 57-63 109 64-70 45 71-77 26 78-84 9

SWTC Student Ages in 2004

15-21 22-28 29-35 36-42 43-49 50-56 57-63 64-70 71-77 78-84 0 200 400 600 800 1000 1200 1400 1600 1800 2000

Ages of SWTC Students in 2004

(54)

1 - 8 8 - 15 15 - 22 22 - 29 29 - 36 36 - 43 0 2 4 6 8 10 12

Joey Lagono NASCAR 2009 Season Finish Results Finish Result F re q u en cy o f O cc u rr en ce

Joey Lagono 2009 Nascar Season

Joey Lagono

(55)

Normally Distributed Data

 Many data collections when graphed produce

a “bell-shaped” curve…

 IQ Test

 mean ( ) = 100

 st. dev ( ) = 15

100 115 85 130 70 55 145 X X X X X X X X X X X X

X X_X

X

X _X

X

x

(56)

Examples

 Information that usually is normally distributed:

 IQ Scores

 Heights

 Measurements taken of a production run of parts.

 Service life of a product (car batteries, tires)

(57)

(58)

(59)

Normally Distributed Data

 Basic Characteristics

symmetry (“bell-shape”) mean ( )

standard deviation (s) or ( )

also median and mode

Small st. dev. ()

large st. dev. ()

x

(60)

Practice

Reading Information

 Given the normal distribution below,

determine the mean _____

42 45 48 51 33 36 39

(61)

Practice

Reading Information

 Both normal distributions shown have a mean

of 20.

 Which one, A or B, has the larger standard

deviation?

20

A

20

(62)

NORMAL

DISTRIBUTIONS

(63)

Normal Distributions and

Percents

 Area under the curve…

 All of the data is located under the curve:

(64)

Normal Distributions and

Percents

 Half of the data is located to the left of the mean:

(65)

Normal Distributions and

Percents

 Half of the data is located to the right of the mean:

(66)

In your notes…

 Write:

 1 – 68%

 2 – 95%

(67)

Normally-distributed Data:

Characteristics

 For any data that is normally distributed:

 68% of the data is located within plus or minus

1 standard deviation from the mean.

s s

(68)

Characteristics

Example –

3.5 L V-6 engine

mean horsepower = 275 hp

standard deviation = 3 hp

275 278 272

68% of the engines built should have a peak horsepower

between 272 and 278.

(

x

)

(



)

(69)

Normally-distributed Data:

Characteristics

For any data that is normally distributed:

95% of the data is located within plus or minus 2 standard deviations from the mean.

s s s s

(70)

Characteristics

Example –

3.5 L V-6 engine

mean horsepower = 275 hp

standard deviation = 3 hp

95% of the engines built should have a peak horsepower

between 269 and 281.

(

x

)

(



)

3 3 3 3

275 281

(71)

Normally-distributed Data:

Characteristics

For any data that is normally distributed:

99.7% of the data is located within +/- 3 standard deviations from the mean.

s s s s s s

(72)

Characteristics

Example –

3.5 L V-6 engine

mean horsepower = 275 hp

standard deviation = 3 hp

99.7% of the engines built

should have a peak horsepower between 266 and 284.

(

x

)

(



)

275 284

266

(73)

Practice

 Test of ultimate strength of welds in 2210-T87

aluminum alloy (1/4” through 1” plate)

39.6 41.8

37.4 44.0 35.2

33.0 46.2

What is the mean for this data?

What is the standard deviation for this data?

39.6 kpsi

2.2

n = 304 n = 304

Units of measure: kpsi

(74)

Practice

Introduction to Normal Distributions

(75)

Statistics

(76)

Using Normally Distributed

Data

 Data on the Heights of U.S. Women

65.5 68

63 70.5

60.5

(77)

Normal Distribution:

Applications

72 month guarantee.

(78)

Using Normally Distributed

Data

 Car Battery Service Life

50 52

48 54

46

44 56

Service Life (Months) of SureStart Car Batteries Service Life (Months) of SureStart Car Batteries

• _{How long does the average}

SureStart Battery last?

• _{Would it be better for this}

company to set a 54 month warranty or a 44 month warranty?

50 months

(79)

Sample Problems

 Data: Lifespan of 60w equiv. light bulbs

20 00 2 15 0 18 50 23 00 17 00 15 50 24 50

As a manufacturer, what would be the safest claim to make about the bulbs?

a) Our bulbs are guaranteed to last 2000 hrs.

b) Our bulbs are guaranteed to last 2300 hrs.

c) Our bulbs are guaranteed to last 1550 hours.

(80)

Sample Problems

 Establish ad campaigns to target products.

19 21

17 23

15

13 25

a) What is the average age of your customers?

b) What percent of your customers are between the ages of 15 and 23?

c) What percent of your customers are over 25 years old?

19 yrs

95%

99.7% between

13 and 25.

100% - 99.7% = 0.3%0.3%  2 = 0.15%

(81)

Establish ad campaigns to target products.

19 21

17 23

15

13 25

d) What percent of your customers are 15 years old or less?

e) If you sold to 15,000 customers last year, how many were between the ages of 17 and 21?

Sample Problems

95% between 15 and 23.100% - 95% = 5%5%  2 = 2.5%

68%68% of 15,000 =

.68 x 15,000 =

(82)

Practice

Normal Distribution Applications

(83)

Statistics

(84)

Correlation

 Is there a link (relationship of cause and

effect) between two things?

Time spent studying…

(85)

Welding

Current HardnessWeld

Ultimate Tensile Strength

(86)

(87)

Correlation

Some more examples

 Is there a link (relationship of cause and

effect) between two things?

Temperature…

(88)

Sample Problem

(89)

STEP 1

(90)

Procedure - Step 1

 Step 1: Create a scatter graph

Size (L) MPG

1.6 26

1.8 27

1.8 26

1.9 26

2.0 25

(91)

Procedure – Step 2

Engine Size vs. Mileage (SUV's)

10 12 14 16 18 20 22 24 26 28

1.5 2.5 3.5 4.5 5.5 6.5 7.5

Engine Size (liters)

M il ea g e (m p g )

Engine Size: 4.0 L

Mileage: 20.5 mpg

Engine Size: 4.0 L

Mileage: 20.5 mpg

Each “dot” represents a vehicle…

…its engine size and mileage.

Each “dot” represents a vehicle…

(92)

Engine Size vs. Mileage (SUV's) 10 12 14 16 18 20 22 24 26 28

1.5 2.5 3.5 4.5 5.5 6.5 7.5

M il ea g e (m p g )

Engine Size: 2.0 L

Mileage: 23.5 mpg

Engine Size: 2.0 L

Mileage: 23.5 mpg

(93)

Procedure – Step 3

10 12 14 16 18 20 22 24 26 28

1.5 2.5 3.5 4.5 5.5 6.5 7.5

(94)

Engine Size vs. Mileage (SUV's) 10 12 14 16 18 20 22 24 26 28

1.5 2.5 3.5 4.5 5.5 6.5 7.5

M il ea g e (m p g ) I II III IV

(95)

Procedure – Step 4

 Quadrant I: _____  Quadrant II: _____  Quadrant III: _____  Quadrant IV: _____

10 12 14 16 18 20 22 24 26 28

1.5 2.5 3.5 4.5 5.5 6.5 7.5

(96)

Quadrant I + Quadrant III = _____

Quadrant II + Quadrant IV = _____

10 12 14 16 18 20 22 24 26 28

1.5 2.5 3.5 4.5 5.5 6.5 7.5

M il ea g e (m p g ) I II III IV Step 6

• _{Positive Correlation}

• _{Negative Correlation}

• _{No Correlation}

Procedure – Step 5

2

12

There is a cause and effect relationship between the two variables.

As one variable increases, so does the variable associated with it.

There is a cause and effect relationship between the two variables.

As one variable increases, the variable associated with it decreases.

There appears to be no relationship

(97)

Procedure – Step 6

 Positive Correlation



  



Temperature

C

rim

e

R

at

(98)

Procedure – Step 6

 Negative Correlation

     

Caffeine Consumption (mg)

(99)

Procedure – Step 6

 No Correlation



(100)

Correlation Criteria

 Correlation Rules _textbook _{page 55}

 Positive

 Sum of Quadrants I and III more than twice the sum of

Quadrants II and IV.

 Negative

 Sum of Quadrants II and IV more than twice the sum of

Quadrants I and III.

 No Correlation

 When neither of the above occur.

Quadrant I + Quadrant III = _____

Quadrant II + Quadrant IV = _____

2

12



10 12 14 16 18 20 22 24 26 28

1.5 2.5 3.5 4.5 5.5 6.5 7.5

(101)

Homework

Correlation