© 2006 baylor university egr 1301 slide 1 lecture 18 statistics approximate running time - 30...
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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$15
=SUM(K2:K13,N2:N13)
=J2^2
=SQRT(N14/23)=N15^2
n
iixx
ndevStd
1
2
1
1..
=SUM(J2:J13,M2:M13)
Slide 14 © 2006 Baylor University
EGR 1301
Graphical Methods
• Describe data on a single variable– Histograms– Pie Charts
• Describe data containing two variables– Scatter Plot
Slide 15 © 2006 Baylor University
EGR 1301
Histogram
• Frequency histogram– Number of data
points in each class
– Plotted vs. each class
Histogram
0
2
4
6
8
10
12
50-59 60-69 70-79 80-89 90-100
Engineering Exam Scores
Fre
qu
ency
Slide 16 © 2006 Baylor University
EGR 1301
Source: Foundations of Engineering, Holtzapple & Reece, 2003
Histogram
• NOTE: Error in text with Figures 9.3, 9.4, & 9.5
Histogram
0
2
4
6
8
10
12
50-59 60-69 70-79 80-89 90-100
Engineering Exam Scores
Fre
qu
ency
Histogram
Frequency Polygon
Slide 17 © 2006 Baylor University
EGR 1301
Histogram
• Relative frequency histogram
nFreq
FreqlRe .
=Q6/$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
Slide 19 © 2006 Baylor University
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