Chapter 3 Displaying and Summarizing Quantitative Data Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 1 3 1 Displaying Quantitative Variables Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 2 Histograms Earthquake Magnitudes The chapter example discusses the magnitudes of earthquakes known to have caused tsunamis from 2000 B C to the present We can display such quantitative data in bins Bins must be equal in width The height of the bin represents the total occurrences between those two values We do this to display the distribution of the quantitative variable Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 3 Histograms Earthquake Magnitudes cont A histogram plots the bin counts as the heights of bars like a bar chart Here is a frequency histogram of these earthquake magnitudes Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 4 Histograms Earthquake Magnitudes cont Here is a relative frequency histogram of these earthquake magnitudes Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 5 Changing the Bin Width and Software In Excel it is up to the user to specify the number of bins and the bin width So this is completely under the control of the user Any good statistical software will automatically pick the number of bins and the bin width but will allow the user to easily change these JMP is one such software package Of the two histograms on the next page which histogram do you prefer Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 6 Changing the Bin Width Cont Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 7 Stem and Leaf Displays Stem and leaf displays show the distribution of a quantitative variable like histograms do while preserving the individual values They are good for relatively small data sets The shape of a stem and leaf plot is exactly the same as a histogram except it is in a vertical format Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 8 Stem and Leaf Example Compare the histogram and stem and leaf display for the pulse rates of 24 women at a health clinic Which graphical display do you prefer Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 9 Stem and Leaf Display and Software There is no simple way to make a stem and leaf display in Excel but they are easily made in JMP JMP displays a legend at the bottom explaining how to read the display Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 10 Constructing a Stem and Leaf Display Manually First cut each data value into leading digits stems and trailing digits leaves Use the stems to label the bins Use only one digit for each leaf either round or truncate the data values if necessary to one decimal place after the stem Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 11 Stem and Leaf In Class Exercise Construct a back to back stem and leaf display of the grades on exam 1 from two small sections of the same graduate class taught by two different professors What differences to you see Who s class would you rather be in Professor A 77 92 100 69 94 74 79 87 86 87 88 Professor B 88 83 95 99 43 99 87 39 50 97 Professor B Professor A 0 2 7 Chapter03 Presentation 0615 10 9 8 7 6 5 4 3 Copyright 2014 2012 2009 Pearson Education Inc 12 Describing a Distribution When describing a distribution make sure to always tell about three things Shape Center Spread Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 13 3 2 Shape Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 14 What is the Shape of the Distribution 1 Does the histogram have a single central hump or several separated humps 2 Is the histogram symmetric 3 Do any unusual features stick out Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 15 Humps 1 Does the histogram have a single central hump or several separated humps Humps in a histogram are called modes most frequent numbers One peak unimodal Two peaks bimodal More than two multimodal A flat histogram without peaks is said to be uniform Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 16 Humps cont A bimodal histogram has two distinct peaks with separation Diastolic Blood Pressure Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 17 Humps cont The uniform histogram can have high points but none of the peaks are distinct from any other peaks Proportion of Wins Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 18 Symmetry 2 Is the histogram symmetric If you can fold the histogram along a vertical line through the middle and have the edges match pretty closely the histogram is symmetric Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 19 Symmetry cont The usually thinner ends of a distribution are called the tails If one tail stretches out farther than the other the histogram is said to be skewed to the side of the longer tail Skewed Left Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc Skewed Right 20 Anything Unusual 3 Do any unusual features stick out You should always mention any stragglers or outliers that stand off away from the body of the distribution Are there any gaps in the distribution If so we might have data from more than one group Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 21 Anything Unusual cont The following histogram has outliers there are three cities in the leftmost bar Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 22 Class Activity Guessing Distribution Characteristics In groups of 2 or 3 discuss what you think the shape of the following distributions are skewed right skewed left or symmetric Also try to guess the minimum and maximum values Data from the Stat 201 Survey Fall 2010 699 students answered the survey The survey is anonymous 12 How many text messages do you typically send on any given day Type 0 if you never send text messages 36 What percentage of people around your age in your preferred gender do you consider dateable 48 On a scale of 1 100 with 100 being the most attractive rate your own attractiveness Chapter03 Presentation 0615 Copyright 2014 2012 2009 Pearson Education Inc 23 3 3 Center Chapter03 Presentation 0615 Copyright 2014 2012
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