1. Lesson 2.1 Graphing Data You will learn to… * display data in a circle graph and a Pareto Graph * organize data in a stem-and-leaf plot and a dot plot * display data in a time series graph

2. Circle Graphs and Bar Graphs are used to display qualitative data.

3. A circle graph shows relationships of parts to a whole. It is easy to compare the size of each part to the whole.

4. Convert the frequency of each class into a percent. Percents are used to label circle graphs. Percent = f n f n then multiply by 100

5. Convert the frequency of each class into a degree. Degrees are used to create circle graphs. angle = percent · 360 ˚

6. n = 60 Cellular Phones Type f Rel Freq. % Angle T-Mobile3 Sprint1 Cingular6 Nextel30 Verizon20 18˚ 6˚ 36˚ 180˚ 120˚ 360˚.05.02.10.50.33 100% 5% 2% 10% 50% 33%

7. Cellular Phones Sprint 2% T-Mobile 5% Cingular 10% Verizon 33% Nextel 50%

8. A Bar Graph displaying qualitative data should be drawn with space between bars of equal width. It is easy to compare the sizes of the parts to each other.

9. n = 60 Cellular Phones Type f Rel Freq. % Angle T-Mobile3 Sprint1 Cingular6 Nextel30 Verizon20 18˚ 6˚ 36˚ 180˚ 120˚ 360˚.05.02.10.50.33 100% 5% 2% 10% 50% 33%

10. Cellular Phones Nextel 35 30 25 20 15 10 5 Number of Phones Type of Service Verizon Cingular T-Mobile Sprint

11. n = 60 Cellular Phones Type f Rel Freq. % Angle T-Mobile3 Sprint1 Cingular6 Nextel30 Verizon20 18˚ 6˚ 36˚ 180˚ 120˚ 360˚.05.02.10.50.33 100% 5% 2% 10% 50% 33%

12. Cellular Phones Nextel Type of Service Verizon Cingular T-Mobile Sprint.70.60.50.40.30.20.10 Relative Frequency

13. A Pareto chart is a bar graph Bars in a Pareto chart are always arranged in descending order

14. Cellular Phones Nextel 35 30 25 20 15 10 5 Number of Phones Type of Service Verizon Cingular T-Mobile Sprint

15. Practice A# 2.1.A

16. We display quantitative data to identify a pattern of variability. One of the simplest graphs used is the dot plot.

17. In a dot plot each data entry is plotted (using a point) above a horizontal axis. It is similar to a bar graph but the display still contains the original data values

18. 60 65 70 75 80 85 90 95 100 Construct a Dot Plot for the following test scores of 20 students. 60 70 90 65 70 70 80 90 85 80 85 85 85 90 70 65 95 85 95 100

19. Stem-and-leaf plots provide an easy way to sort data. Each number is separated into a “stem” Similar to a bar graph but the display still contains the original data values

20. Stem-and-Leaf Plot Key Key: 4 | 5 = 45 Key: 11 | 6 = 116 Key: 12 | 3 = 12.3 Data entries with 1 digit after the decimal Two digit data entries Three digit data entries Always use consecutive integers for stems. If there is no data for a stem, the leaf part is empty.

21. 50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 88 41 78 56 72 56 17 7 Number of Minutes on the Internet Stem-and-Leaf Plot What stems should we use?

22. 012345678012345678 Key: 1| 6 = 16 Number of Minutes on the Internet

23. 50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 88 41 78 56 72 56 17 7 Number of Minutes on the Internet

24. 0 7 7 1 7 1 9 7 2 2 8 1 3 3 7 4 0 1 4 2 1 5 0 1 4 6 6 6 7 8 2 8 Key: 1| 6 = 16 Now, order the data Number of Minutes on the Internet

25. 0 7 7 1 7 1 9 7 2 2 8 1 3 3 7 4 0 1 4 2 1 5 0 1 4 6 6 6 7 8 2 8 Key: 1| 6 = 16 Number of Minutes on the Internet Does the Plot look like a bar graph?

26. Construct a stem-and-leaf plot and a dot plot for the following data set. 805290525355708291 555571827491827455 758593859376567693

27. 5 2 2 3 4 5 5 5 5 6 6 7 0 1 4 4 5 6 6 8 0 2 2 2 5 5 9 0 1 1 3 3 3 Key: 6|4 is 64 50 55 60 65 70 75 80 85 90 95

28. Practice A# 2.1.B

30. A time series graph is a line graph used to show a pattern that occurs over a period of time Horizontal axis: year/month Vertical axis: number or percent

31. time series graph > gas prices each week for 3 months > # students enrolled at RV > winning times in an Olympic race for the last 10 Olympics > sales each month of one year

32. Month JFMAMJJASOND Average price for a gallon of gas $1.85$1.77$1.80$1.86$1.95$2.05$2.15$2.25$2.05$2.15 $2.25 $2.30 J F M A M J J A S O N D 2.40 2.30 2.20 2.10 2.00 1.90 1.80 1.70 1.60 Gas Price per gallon MONTH Average Price Per Gallon of Gasoline

33. Practice A# 2.2.C