Lecture 18
Statistics
Approximate Running Time - 30 minutes
Distance Learning / Online Instructional Presentation
Presented by
Department of Mechanical Engineering
Baylor University
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EGR 1301
Slide 1
© 2006 Baylor University
Introduction
Dr. Carolyn Skurla
Speaking
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Slide 2
© 2006 Baylor University
What is Statistics?
• The study of making sense of data
• Almost everyone deals with data
– CEOs
– Scientists
– Consumers
– Engineers
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Slide 3
© 2006 Baylor University
Making Sense of Data
• Scientific methods for:
– Collecting data
– Organizing data
– Summarizing data
– Presenting data
– Analyzing data
– Drawing conclusions
EGR 1301
Slide 4
© 2006 Baylor University
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
EGR 1301
Slide 5
© 2006 Baylor University
Common Statistical Tools
•
•
•
•
•
Descriptive statistics
Histograms
Pie charts
Bar charts
Scatter plots
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Slide 6
© 2006 Baylor University
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
EGR 1301
Slide 7
© 2006 Baylor University
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
EGR 1301
Slide 8
© 2006 Baylor University
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
EGR 1301
Slide 9
© 2006 Baylor University
Measures of
Central Tendency
1911
Mean 
 79.6
• Mean
24
– Arithmetic average
• Median
– Odd # of obs = middle
value of sorted data
– Even # of obs = mean of 2
middle values
• Mode Mode  85
– Value that appears most
frequently
Slide 10
© 2006 Baylor University
85  83
Median 
 84
2
=G14/F13
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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
Slide 11
© 2006 Baylor University
Source: An Introduction to Statistical Methods and Data Analysis, Ott, 1993
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Measures of
Spread of the Data
• Range
Range  99  55  44
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Slide 12
© 2006 Baylor University
Measures of
Spread of the Data
=J2^2
• Range
=E2-$G$15
• Deviation
• Standard deviation
1
Std .dev. 
 x  x 
n 1
• Variance
n
i 1
2
i
=SUM(J2:J13,M2:M13)
=SUM(K2:K13,N2:N13)
=SQRT(N14/23)
=N15^2
Slide 13
© 2006 Baylor University
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Graphical Methods
• Describe data on a single variable
– Histograms
– Pie Charts
• Describe data containing two variables
– Scatter Plot
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Slide 14
© 2006 Baylor University
Histogram
• Frequency
histogram
Histogram
12
10
8
Frequency
– Number of data
points in each
class
– Plotted vs. each
class
6
4
2
0
50-59
60-69
70-79
80-89
Engineering Exam Scores
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Slide 15
© 2006 Baylor University
90-100
Histogram
• NOTE: Error in text with Figures 9.3, 9.4, & 9.5
Frequency Polygon
Histogram
12
10
Frequency
8
6
4
2
0
Source: Foundations of Engineering, Holtzapple & Reece, 2003
50-59
60-69
70-79
80-89
90-100
Engineering Exam Scores
Histogram
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Slide 16
© 2006 Baylor University
Histogram
=Q6/$Q$7
• Relative frequency
histogram
Freq
Rel.Freq 
n
Relative Frequency Histogram
0.45
0.40
Relative Frequency
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
50-59
60-69
70-79
80-89
Engineering Exam Scores
Slide 17
© 2006 Baylor University
90-100
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Histogram
=R6+S5
• Relative
cumulative
frequency
histogram
1.0
Relative Cumulative Frequency
– Accumulated
sum of relative
frequencies
Relative Cumulative Frequency Histogram
0.8
0.6
0.4
0.2
0.0
50-59
60-69
70-79
80-89
Engineering Exam Scores
EGR 1301
Slide 18
© 2006 Baylor University
90-100
Pie Chart
Pie Chart of Engineering Exam Scores
90-100
17%
50-59
8%
60-69
13%
70-79
21%
80-89
41%
EGR 1301
Slide 19
© 2006 Baylor University
Scatter Plot
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Slide 20
© 2006 Baylor University