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. c. 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 8 9 9 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 8 9 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.

70 90 105 110 130 150 155 160

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?

Cars Trucks Motorcycles Other f 20,818 12,001 2,472 515 R elative Frequency 0.58

0.34

0.07

0.01

Angle 209 o 132 o 25 o 4 o

Motor Vehicle Occupants Killed in 1999

Occupants Killed Motorcycles 7% Other 1% Trucks 34% Cars 58%

Cars Trucks Motorcycles 4th Qtr

Try it Yourself

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 Cars Trucks Motorcycles Other Killed 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?

18 16 14 12 10 8 6 4 2 0

Solution

Causes of Inventory Shrinkage

Causes of Inventory Shrinkage

Try it Yourself

Every year the Better Business Bureau receives complaints from dissatisfied customers. In a recent year they received the following complaints.

7792Complaints 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

Section 2.2

More Graphs and Displays

Stem-and-Leaf Plot

Lowest value is 67 and highest value is 125, so list stems from 6 to 12.

102 124 108 86 103 82

Stem 6 | 7 | 8 | 9 | 10 | 11 | 12 | Leaf 6 2 4 2 8 3

To see complete display, go to next slide.

Stem-and-Leaf Plot

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

Stem-and-Leaf with two lines per stem

Key: 6 | 7 means 67

1st line digits 0 1 2 3 4 2nd line digits 5 6 7 8 9 1st line digits 0 1 2 3 4 2nd line digits 5 6 7 8 9

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

Dot Plot

Phone

66 76 86 96 minutes 106 116 126

Pie Chart

• • Used to describe parts of a whole Central Angle for each segment NASA budget (billions of $) divided among 3 categories.

Billions of $ Human Space Flight 5.7

Technology 5.9

Mission Support 2.7

Construct a pie chart for the data.

Human Space Flight Technology Mission Support

Total

Mission Support 19%

Pie Chart

Billions of $

5.7

5.9

2.7

14.3

Degrees

143 149 68 360 Human Space Flight 40% NASA Budget (Billions of $) Technology 41%

Scatter Plot

Absences

x

8 2 5 12 15 9 6 Final grade (y) 95 90 85 80 75 70 65 60 55 50 45 40 0 2 4 6 8 Absences (x) 10 12 14 16 Grade

y

78 92 90 58 43 74 81