© 2006 Baylor University EGR 1301 Slide 1 Lecture 18 Statistics Approximate Running Time - 30 minutes Distance Learning / Online Instructional Presentation Presented by Department of Mechanical Engineering Baylor University Procedures: 1.Select “Slide Show” with the menu: Slide Show|View Show (F5 key), and hit “Enter” 2.You will hear “CHIMES” at the completion of the audio portion of each slide; hit the “Enter” key, or the “Page Down” key, or “Left Click” 3.You may exit the slide show at any time with the “Esc” key; and you may select and replay any slide, by navigating with the “Page Up/Down” keys, and then hitting “Shift+F5”.

© 2006 Baylor University EGR 1301 Slide 2 Introduction Dr. Carolyn Skurla Speaking

© 2006 Baylor University EGR 1301 Slide 3 What is Statistics? The study of making sense of data Almost everyone deals with data –CEOs –Scientists –Consumers –Engineers

© 2006 Baylor University EGR 1301 Slide 4 Making Sense of Data Scientific methods for: –Collecting data –Organizing data –Summarizing data –Presenting data –Analyzing data –Drawing conclusions

© 2006 Baylor University EGR 1301 Slide 5 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

© 2006 Baylor University EGR 1301 Slide 6 Common Statistical Tools Descriptive statistics Histograms Pie charts Bar charts Scatter plots

© 2006 Baylor University EGR 1301 Slide 7 Measures of Central Tendency Mean (µ) –Arithmetic average Median (M d ) –Central value Mode (M o ) –Most frequently occurring value Source: An Introduction to Statistical Methods and Data Analysis, Ott, 1993

© 2006 Baylor University EGR 1301 Slide 8 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

© 2006 Baylor University EGR 1301 Slide 9 Measures of Central Tendency Typically sort the data –Allows categories or classes to be assigned A = B = C = D = F < 60 –Generally, select 5-20 classes with each data point only fitting into one class

© 2006 Baylor University EGR 1301 Slide 10 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 =G14/F13

© 2006 Baylor University EGR 1301 Slide 11 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

© 2006 Baylor University EGR 1301 Slide 12 Measures of Spread of the Data Range

© 2006 Baylor University EGR 1301 Slide 13 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 =SUM(J2:J13,M2:M13)

© 2006 Baylor University EGR 1301 Slide 14 Graphical Methods Describe data on a single variable –Histograms –Pie Charts Describe data containing two variables –Scatter Plot

© 2006 Baylor University EGR 1301 Slide 15 Histogram Frequency histogram –Number of data points in each class –Plotted vs. each class

© 2006 Baylor University EGR 1301 Slide 16 Source: Foundations of Engineering, Holtzapple & Reece, 2003 Histogram NOTE: Error in text with Figures 9.3, 9.4, & 9.5 Histogram Frequency Polygon

© 2006 Baylor University EGR 1301 Slide 17 Histogram Relative frequency histogram =Q6/$Q$7

© 2006 Baylor University EGR 1301 Slide 18 Histogram Relative cumulative frequency histogram –Accumulated sum of relative frequencies =R6+S5

© 2006 Baylor University EGR 1301 Slide 19 Pie Chart

© 2006 Baylor University EGR 1301 Slide 20 Scatter Plot