Slide 1 © 2006 Baylor University

EGR 1301

Lecture 18Statistics

Approximate Running Time - 30 minutesDistance Learning / Online Instructional Presentation

Presented byDepartment of Mechanical Engineering

Baylor University

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Slide 2 © 2006 Baylor University

EGR 1301

Introduction

Dr. Carolyn Skurla

Speaking

Slide 3 © 2006 Baylor University

EGR 1301

What is Statistics?

• The study of making sense of data

• Almost everyone deals with data– CEOs– Scientists– Consumers– Engineers

Slide 4 © 2006 Baylor University

EGR 1301

Making Sense of Data

• Scientific methods for:– Collecting data– Organizing data– Summarizing data– Presenting data– Analyzing data– Drawing conclusions

Slide 5 © 2006 Baylor University

EGR 1301

Why Study Statistics?

• You need to know how to evaluate published numerical facts– Manufacturer claims

• “4 out of 5 dentists”

– Political polls– Some claims are valid & some are not

• Your profession may require you to:– Interpret the results of sampling– Employ statistical methods of analysis to make

inferences in your work

Slide 6 © 2006 Baylor University

EGR 1301

Common Statistical Tools

• Descriptive statistics

• Histograms

• Pie charts

• Bar charts

• Scatter plots

Slide 7 © 2006 Baylor University

EGR 1301

Measures of Central Tendency

• Mean (µ)– Arithmetic average

• Median (Md)

– Central value

• Mode (Mo)

– Most frequently occurring value

Source: An Introduction to Statistical Methods and Data Analysis, Ott, 1993

Slide 8 © 2006 Baylor University

EGR 1301

Measures of Central Tendency

• Figure 9.2, pg. 233– MS Excel example– 24 student scores on

an engineering exam– Raw data is in random

order

Slide 9 © 2006 Baylor University

EGR 1301

Measures of Central Tendency

• Typically sort the data– Allows categories or

classes to be assigned• A = 90-100• B = 80-89• C = 70-79• D = 60-69• F < 60

– Generally, select 5-20 classes with each data point only fitting into one class

Slide 10 © 2006 Baylor University

EGR 1301

Measures of Central Tendency

• Mean– Arithmetic average

• Median– Odd # of obs = middle

value of sorted data– Even # of obs = mean of 2

middle values

• Mode– Value that appears most

frequently

6.7924

1911 Mean

85Mode

842

8385 Median=G14/F13

Slide 11 © 2006 Baylor University

EGR 1301

Measures of Spread of the Data

• Range– Subtract min from max

• Deviation– Sums to zero

• Mean absolute deviation– Not commonly used

• Standard deviation– Dev squared, summed,

square root of sum divided by n-1

• Variance– Std dev squared

Source: An Introduction to Statistical Methods and Data Analysis, Ott, 1993

Slide 12 © 2006 Baylor University

EGR 1301

Measures of Spread of the Data

• Range445599 Range

Slide 13 © 2006 Baylor University

EGR 1301

Measures of Spread of the Data

• Range• Deviation• Standard deviation

• Variance

=E2-$G$15

=SUM(K2:K13,N2:N13)

=J2^2

=SQRT(N14/23)=N15^2

n

iixx

ndevStd

1

2

1

1..

=SUM(J2:J13,M2:M13)

Slide 14 © 2006 Baylor University

EGR 1301

Graphical Methods

• Describe data on a single variable– Histograms– Pie Charts

• Describe data containing two variables– Scatter Plot

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EGR 1301

Histogram

• Frequency histogram– Number of data

points in each class

– Plotted vs. each class

Histogram

0

2

4

6

8

10

12

50-59 60-69 70-79 80-89 90-100

Engineering Exam Scores

Fre

qu

ency

Slide 16 © 2006 Baylor University

EGR 1301

Source: Foundations of Engineering, Holtzapple & Reece, 2003

Histogram

• NOTE: Error in text with Figures 9.3, 9.4, & 9.5

Histogram

0

2

4

6

8

10

12

50-59 60-69 70-79 80-89 90-100

Engineering Exam Scores

Fre

qu

ency

Histogram

Frequency Polygon

Slide 17 © 2006 Baylor University

EGR 1301

Histogram

• Relative frequency histogram

nFreq

FreqlRe .

=Q6/$Q$7

Relative Frequency Histogram

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

50-59 60-69 70-79 80-89 90-100

Engineering Exam Scores

Rel

ativ

e F

req

uen

cy

Slide 18 © 2006 Baylor University

EGR 1301

Histogram

• Relative cumulative frequency histogram– Accumulated

sum of relative frequencies

Relative Cumulative Frequency Histogram

0.0

0.2

0.4

0.6

0.8

1.0

50-59 60-69 70-79 80-89 90-100

Engineering Exam Scores

Rel

ativ

e C

um

ula

tive

Fre

qu

ency

=R6+S5

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EGR 1301

Pie Chart

Pie Chart of Engineering Exam Scores

50-598%

60-6913%

70-7921%

80-8941%

90-10017%

Slide 20 © 2006 Baylor University

EGR 1301

Scatter Plot