1Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.Chapter 5 Understanding and Comparing DistributionsChapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.2The Big Picture Below is a histogram of the Average Wind Speed for every day in 1989.Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.3The Big Picture (cont) Which direction is this distribution skewed? The high value (8.67) may be an outlier. Median daily wind speed is 1.90 mph and the IQR is 1.78 mph. Can we say more?Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.4The Five-Number Summary The five-number summaryof a distribution reports its median, quartiles, and extremes (maximum and minimum).Max 8.67Q3 2.93Median 1.90Q1 1.15Min 0.20Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.5Daily Wind Speed: Making Boxplots A boxplot: is a graphical display of the five-number summary of a data set, and makes a judgment about whether or not there are potential outliers in the data set. Boxplots are particularly useful when comparing groups.Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.6Constructing Boxplots1. Draw a single vertical axis spanning the range of the data.2. Draw short horizontal lines at the lower and upper quartiles and at the median.3. Then connect them with vertical lines to form two boxes.Max 8.67Q3 2.93Median 1.90Q1 1.15Min 0.20Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.7Constructing Boxplots (cont.)4. Erect “fences” around the main part of the data. The upper fence is 1.5 IQRs above the upper quartile. The lower fence is 1.5 IQRs below the lower quartile.Max 8.67Q3 2.93Median 1.90Q1 1.15Min 0.20Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.8Constructing Boxplots (cont.)5. Use the fences to grow “whiskers.” Draw lines from the ends of the box up and down to the most extreme data values found within the fences.Max 8.67Q3 2.93Median 1.90Q1 1.15Min 0.20Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.9Constructing Boxplots (cont.)6. Add the outliers by displaying any data values beyond the fences with special symbols. Some software packages use a different symbol for “far outliers” that are farther than 3 IQRsfrom the quartiles.Max 8.67Q3 2.93Median 1.90Q1 1.15Min 0.20Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.10Constructing Boxplots (cont.)The final boxplot does not display the “fences”.Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.11Wind Speed: Making Boxplots (cont.) Compare the histogram and boxplot for daily wind speeds: How does each display represent the distribution?Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.12Class Activity – Drawing a Box Plot On the next page you will see a sample of some data collected from a previous Stat 201 class. It represent the number of Facebook Friends these 32 students reported they had (the data are already sorted). You will also find some summary statistics needed to construct the box plot. After drawing your box plot, compare your work with your teammate.Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.130500100015002000250030003500IQR = Q3 – Q1 Upper Fence = Q3 + 1.5(IQR) Lower Fence = Q1 - 1.5(IQR)Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.14Comparing Groups Boxplots can be plotted side by side for groups or categories we wish to compare. What do these boxplots tell you?Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.15Comparing Groups (Cont.) When making comparisons with histograms, make sure the horizontal scales are the same! The data used for the example on the next page represents the number of cigarettes (hundreds) made per day by 2 different machines over a 30 day period. Which set of histograms makes the differences between these two machines clear?Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.16Default Output Common Horizontal ScalesChapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.17Timeplots: Order, Please! For some data sets, we are interested in how the data behave over time. In these cases, we construct timeplotsof the data.Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.18Smoothing Timeplots Timeplots with lots of point-to-point variation are difficult to see the overall trends in the data. A smooth trace of the data can be added to help see the overall trends that exist.Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.19Smoothing Timeplots (Cont.) A moving average of the original data is one way to smooth the data.Original Data 5-Item Moving Average15-Item Moving AverageChapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.20Other Statistical Topics Related toTime Ordered Data Time Series Analysis - looking for patterns in time ordered data. Issues such as the existences of seasonality, long-term trends and the impact of the economy are addressed to allow for making reasonable forecasts of the future. At UT, Statistics 475 is devoted to this topic. Statistical Process Control (SPC) - using time ordered data to help businesses improve the quality of their services and/or products. At UT, Statistics 340 contains material on this topic.Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.21Other Statistical Topics Related toTime Ordered Data (Cont.) The primary tool of SPC is the “Control Chart”. A control chart is a timeplot with the average and “Control Limits” reported. The control limits define the amount of variation in the data that can be attributed to “chance” variation. Points outside the control limits probably have some sort of explanation for their behavior.Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.22Beware of Misleading Timeplots Time is on the x-axis in this image. What is on the y-axis?Chapter05 Presentation 1213Copyright © 2009 Pearson Education, Inc.23Histograms vs. Timeplots Winning Times in the Kentucky Derby (in Seconds) from 1896 to 2008. What does the timeplot (run chart) reveal that the histogram does
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