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

SolutionBecause 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 2Constructing Variations of Stem and leaf PlotsOrganize 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 twiceb. List all leaves using the appropriate stem

row.

Example 3Constructing 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 140126 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 90 110 130 150160155105

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 SetsConstructing a Pie ChartThe number of motor vehicle occupants killed in

the table. Use a Pie Chart to organize the data. What can you conclude?

f Relative Frequency

Angle

CarsTrucksMotorcyclesOther

20,81812,001 2,472 515

0.58 0.34 0.07 0.01

209o

132o

25o

4o

Motor Vehicle Occupants Killed in 1999

Occupants Killed

CarsTrucksMotorcycles4th Qtr

Trucks 34%

Other 1%

Cars 58%

Motorcycles 7%

34%

Try it YourselfThe 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

CarsTrucks MotorcyclesOther

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

Employee Theft

Shoplift

iing

Administrati

ve Erro

r

Vendor Frau

d02468

1012141618

Causes of Inventory Shrinkage

Causes of Inventory Shrinkage

Try it YourselfEvery year the Better Business Bureau receives

complaints from dissatisfied customers. In a recent year they received the following complaints.

7792Complaints about home furnishing stores5733 Complaints about computer sales and service

stores14,668 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

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

2

4

8

6

3

2

Stem Leaf

To see complete display, go to next slide.

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

Stem-and-Leaf Plot

Key: 6 | 7 means 67

Stem-and-Leaf with two lines per stem

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

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

Dot Plot

66 76 86 96 106 116 126

Phone

minutes

NASA budget (billions of $) divided among 3 categories.

Pie Chart• Used to describe parts of a whole• Central Angle for each segment

Construct a pie chart for the data.

Human Space Flight 5.7Technology 5.9Mission Support 2.7

Billions of $

NASA Budget(Billions of $)

HumanSpace Flight

40%

Total

Pie ChartBillions of $

Human Space Flight 5.7Technology 5.9Mission Support 2.7

14.3

Degrees

143149 68

360MissionSupport

19%

Technology41%

Scatter PlotAbsences Grade

0 2 4 6 8 10 12 14 16

404550556065707580859095

Absences (x)

x825

121596

y78929058437481

Finalgrade

(y)