1. 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.

2. 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 q

3. 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.

4. RBIs for American league Leaders
Key = 155 8 9
Unordered stem and leaf Plot

5. RBIs for American league Leaders
Key = 155 8 9
Ordered stem and leaf Plot

6. 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.

7. 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?

8. RBIs for American league Leaders
Key = 155 7 8 9 10
Unordered stem and leaf Plot

9. RBIs for American league Leaders
Key = 155 8 9
Ordered stem and leaf Plot

10. 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.

11. Example 3
Constructing a Dot Plot Use a dot plot to organize the RBI data given in example

12. 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 The value that occurs the most is 126.

13. 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.

14. 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

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

16. 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

17. 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.

18. 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?

19. Solution

20. 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?

21. Homework 1-14, odd pgs.53-56

22. More Graphs and Displays
Section 2.2
More Graphs and Displays

23. 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.
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

24. 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 |
9 |
10 |
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.

25. Stem-and-Leaf with two lines per stem
Key: 6 | 7 means 67
6 | 7
7 | 1
7 | 8
8 | 2
8 |
9 | 2
9 |
10 |
10 |
11 | 2
11 | 6 8
12 | 2 4
12 | 5
1st line digits
2nd line digits
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
2nd line digits

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

27. 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
Technology
Mission Support
Construct a pie chart for the data.

28. 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%

29. 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)