Section 2-2 More graphs and Displays Objective: SWBAT Graph and interpret quantitative Data sets using stem and leaf plots And dot plots. Also be able to graph and interpret quantitative data sets using pie charts and Pareto charts. How to graph and interpret paired data sets using scatter plots, and time series charts.

Graphing Quantitative Data Sets Constructing a stem and leaf plot The following are the numbers of league leading Runs batted in (RBIs) for baseballs American League during a recent 50 yeafr period. Display the data in a Stem and leaf plot. What can you conclude. 155 159 144 129 105 145 1q26 116 139 114 122 112 112 142 126 118 118 108 122 121 109 140 126 119 113 117 118 109 109 119 139 139 122 78 133 126 123 145 121 134 124 119 132 133 124 129 112 126 148 147

Solution Because the data entries go from a low of 78 to a high of 159 use stem values from 7 to 15. To construct the plot list those stems to the left of a vertical line. For each data entry list a leaf to the right of its stem. For instance the entry 155 has a stem of 15 and a leaf of 5. The resulting stem and leaf plot will be unordered. To obtain an ordered stem and leaf plot , rewrite the plot with the leaves in increasing order. From left to right. It is important to include a key for the display to identify the values of the data.

RBIs for American league Leaders 7 8 Key 15 5 = 155 8 9 10 5 8 9 9 9 11 6 4 2 2 8 8 9 3 7 8 9 9 2 12 9 6 2 6 2 1 6 2 6 3 1 4 4 9 6 13 0 9 9 3 4 2 3 14 4 5 2 0 5 8 7 15 5 9 Unordered stem and leaf Plot

RBIs for American league Leaders 7 8 Key 15 5 = 155 8 9 10 5 8 9 9 9 11 2 2 2 3 4 6 7 8 8 8 9 9 9 12 1 1 2 2 2 3 4 4 6 6 6 6 6 9 9 13 0 2 3 3 4 9 9 14 0 2 4 5 5 7 8 15 5 9 Ordered stem and leaf Plot

Try it yourself Use a stem and leaf plot to organize the Akhiok population data set listed on page 30. What can you conclude? a. List all possible stems. b.List the leaf of each data entry to the right of its stem and include a key. Rewrite the stem and leaf plot so that it is ordered. d. Use the plot to ma a conclusion.

Example 2 Constructing Variations of Stem and leaf Plots Organize the data given in example 1 using a stem and leaf plot that has two lines for each stem. What can you conclude?

RBIs for American league Leaders 7 8 Key 15 5 = 155 7 8 9 10 10 5 8 9 9 9 11 4 2 2 3 2 11 6 4 2 2 8 8 9 3 7 8 9 9 2 12 9 6 2 6 2 1 6 2 6 3 1 4 4 9 6 13 0 9 9 3 4 2 3 14 4 5 2 0 5 8 7 15 5 9 Unordered stem and leaf Plot

RBIs for American league Leaders 7 8 Key 15 5 = 155 8 9 10 5 8 9 9 9 11 2 2 2 3 4 6 7 8 8 8 9 9 9 12 1 1 2 2 2 3 4 4 6 6 6 6 6 9 9 13 0 2 3 3 4 9 9 14 0 2 4 5 5 7 8 15 5 9 Ordered stem and leaf Plot

Try it yourself Using two rows for each stem revise the stem and leaf plot you constructed for Try it Yourself 1. a. List each stem twice b. List all leaves using the appropriate stem row.

Example 3 Constructing a Dot Plot Use a dot plot to organize the RBI data given in example 1. 155 159 144 129 105 145 126 116 130 114 122 112 112 142 126 118 118 108 122 121 109 140 126 119 113 117 118 109 109 119 139 122 76 133 126 123 145 121 134 124 119 132 133 124 129 112 126 148 147

So that each entry is included in the dot plot the horizontal axis should include numbers between 70 and 160. To represent a data entry plot a point above the the entry’s position on the axis, If an entry is repeated plot another point above the previous point. 160 70 90 155 110 150 105 130 From the dot plot you can see that most of the points cluster around 105 and 148. The value that occurs the most is 126.

Try This Yourself Use a dot plot to organize the data listed in the chapter opener on page 30. What can you conclude from the graph? a. Choose an appropriate scale for the horizontal axis. b. Represent each data entry by plotting a point for each entry. c. Describe any patterns for the data.

Graphing Quantitative data Sets Constructing a Pie Chart The number of motor vehicle occupants killed in the table. Use a Pie Chart to organize the data. What can you conclude? f R elative Frequency Angle Cars Trucks Motorcycles Other 20,818 12,001 2,472 515 0.58 0.34 0.07 0.01 209o 132o 25o 4o

Motor Vehicle Occupants Killed in 1999 Motorcycles 7% Cars 58% 34%

Try it Yourself Vehicle Type The number of motor vehicles Occupants killed in 1989 are listed in the table. Use a Pie chart to organize the data. Compare the 1989 data to the 1999 data. Vehicle Type Killed Cars Trucks Motorcycles Other 25,063 9,409 3,141 474

Pareto Chart Another way to graph qualitative data is with a Pareto Chart. A pareto Chart is a vertical bar graph in which the height of each bar represents the frequency or relative frequency. The bars are positioned in decreasing order of decreasing height with the tallest bar positioned at the left. Such positioning helps highlight important data and is used frequently in Business.

Example 5 Constructing a Pareto Chart In a recent year the retail industry lost $41.0 million in inventory shrinkage. Inventory shrinkage is the loss of inventory through breakage, pilfering , shoplifting, and so on.The causes of inventory shrinkage are administrative error($7.8million),employee theft($15.6million),shoplifting($14.7million), vendor fraud($2.9 million). If you were a retailer which causes of inventory shrinkage would you address first?

Solution

Try it Yourself Every year the Better Business Bureau receives complaints from dissatisfied customers. In a recent year they received the following complaints. Complaints about home furnishing stores 5733 Complaints about computer sales and service stores 14,668 Complaints about auto dealers. 9728 Complaints about auto repair shops. 4649 Complaints about dry cleaning companies. Use a Pareto Chart to organize the data. What source is the greatest cause of complaints?

Homework 1-14, 15-29 odd pgs.53-56

More Graphs and Displays Section 2.2 More Graphs and Displays

Stem-and-Leaf Plot 6 | 7 | 8 | 9 | 10 | 11 | 12 | Lowest value is 67 and highest value is 125, so list stems from 6 to 12. 102 124 108 86 103 82 Stem Leaf 6 | 7 | 8 | 9 | 10 | 11 | 12 | 6 2 Divide each data value into a stem and a leaf. The leaf is the rightmost significant digit. The stem consists of the digits to the left. The data shown represent the first line of the ‘minutes on phone’ data used earlier. The complete stem and leaf will be shown on the next slide. 2 8 3 To see complete display, go to next slide. 4

Stem-and-Leaf Plot Key: 6 | 7 means 67 6 | 7 7 | 1 8 8 | 2 5 6 7 7 6 | 7 7 | 1 8 8 | 2 5 6 7 7 9 | 2 5 7 9 9 10 | 0 1 2 3 3 4 5 5 7 8 9 11 | 2 6 8 12 | 2 4 5 Key: 6 | 7 means 67 Stress the importance of using a key to explain the plot. 6|7 could mean 6700 or .067 for a different problem. A stem and leaf should not be used with data when values are very different such as 3, 34,900, 24 etc. The stem-and leaf has the advantage over a histogram of retaining the original values.

Stem-and-Leaf with two lines per stem Key: 6 | 7 means 67 6 | 7 7 | 1 7 | 8 8 | 2 8 | 5 6 7 7 9 | 2 9 | 5 7 9 9 10 | 0 1 2 3 3 4 10 | 5 5 7 8 9 11 | 2 11 | 6 8 12 | 2 4 12 | 5 1st line digits 0 1 2 3 4 2nd line digits 5 6 7 8 9 With two lines per stem the data is more finely “chopped”. Class width is 5 times the leaf unit. All stems except possibly the first and last must have two lines even if one is blank. For this data set, the first line for the stem 6 can be blank because there are no data values from 60 to 64. 1st line digits 0 1 2 3 4 2nd line digits 5 6 7 8 9

Dot Plot Phone 66 76 86 96 106 116 126 minutes Dot plots also allow you to retain original values.

NASA budget (billions of $) divided among 3 categories. Pie Chart Used to describe parts of a whole Central Angle for each segment NASA budget (billions of $) divided among 3 categories. Pie charts help visualize the relative proportion of each category. Find the relative frequency for each category and multiply it by 360 degrees to find the central angle. Billions of $ Human Space Flight 5.7 Technology 5.9 Mission Support 2.7 Construct a pie chart for the data.

Pie Chart Human Space Flight 5.7 143 Technology 5.9 149 Billions of $ Degrees Human Space Flight 5.7 143 Technology 5.9 149 Mission Support 2.7 68 14.3 360 Total Mission Support 19% Human Space Flight 40% NASA Budget (Billions of $) Technology 41%

Scatter Plot Absences Grade x 8 2 5 12 15 9 6 y 78 92 90 58 43 74 81 Final grade (y) 40 45 50 55 60 65 70 75 80 85 90 95 2 4 6 8 10 12 14 16 Absences (x)