1. Stat 2411 Statistical Methods Chapter 2: Summarizing data

2. Summarizing Data Data are collected to answer some questions. The analysis of the data includes thinking and statistical methods. Example: 8 lb test Fishing Line Question: Which type(s) of line are strongest?

3. 2.1 Listing numerical data Trilene XL 11.5 11.3 11.7 11.6 11.7 11.411.511.511.611.4 Trilene XT 11.611.811.711.711.5 11611.611.811.411.7 Stren 11.111.111.211.011.1 11.311.210.911.011.1

4. Plotting of the data Dot diagram When Analyzing data, always plot the data! A dot diagram: XLXTStren 11.8* * 11.7* ** * * 11.6* ** * * 11.5* * ** 11.4* ** 11.3* * 11.2 * * 11.1 * * * * 11.0 * * 10.9 *

5. Plotting of the data Bar Chart A bar chart – Trilene XL 11.311.411.511.611.7

6. 2.2 Stem and Leaf Diagram 1)Separate each observation into 2 parts Stem: everything but the rightmost digit Leaf: the final digit 2)Write the stems in a vertical column, then draw a vertical line next to them 3)Write each leaf in a row to the right of its stem

7. Stem Leaf plot 9 10 11 12 13 Systolic bp data 108 134 100 108 112 112 112 122 116 116 120 108 108 96 114 108 128 114 112 124 90 102 106 124 130 116 8 2 0 4 8 2

8. Completed Stem Leaf plot 9 10 11 12 13 06 02688888 222244666 02448 04

9. Stem and Leaf Diagram Exercise Cardiac output in middle aged runners. (Journal of Sports Medicine) 20.917.919.916.012.823.221.2 21.020.915.022.222.218.319.8 21.015.823.620.6 Tip: Stem—Ones Leaves—Tenths 12. 8 13. 14. 15. 0 8 16. 0 17. 9 18. 3 19. 8 9 20. 6 9 9 21. 0 0 2 6 9 22. 2 2 23. 6

10. 2.3 Frequency Distributions With larger data sets it helps to count numbers of values in different summary classes, usually 5-15 classes. E.g. Suspended solids in agricultural watersheds. (Water Resources Bulletin) Suspended Solids (ppm)Frequency 30-39 8 40-49 7 50-69 5 60-69 11 70-79 6 80-89 1 90-99 2

11. Frequency Distributions Look at book for: –Class limits –Upper class limits –Lower class limits –Class marks –Class intervals

12. 2.4 Graphical Representations A histogram represents a frequency distribution with bars. 8 7 5 11 6 1 2 30-3940-4950-5960-6970-7980-8990-99

13. Pie Chart (360 x %) Tree#%Degrees Oak5062.5%225 Maple2025%90 Ash1012.5%45 80360

14. 2.5 Two Variable Data Scattergram Cma Chromosome Abnormal % 0.112 0.195 0.5113 0.5315 1.0825 1.6228 1.7336 2.3645 2.7256 3.1259 3.8863 4.1860

15. Two groups can be compared with back to back stem and leaf diagrams E.g. Stopping distances of bikes Treaded tireSmooth tire 341 8 9 355 536 6 4375 38 1391 2 040 Or dot diagrams | | | * | ** | | * |**Treaded 340350 360 370 380 390400 |*** | * | | * | | * |Smooth

16. When there are associations between sets of data values, plot the data accordingly. E.g., Snowfall for duluth and White Bear Lake 1972-2000 A not very good way to plot the data WB Lake Duluth 130* 120* 110** ** 100*** * 90***** 80****** ****** 70** *** 60** ********** 50**** *** 40*** *** 30* *** 20

17. Duluth White Bear

18. A study of trace metals in South Indian River 1 2 3 4 5 6 T=top water zinc concentration (mg/L) B=bottom water zinc (mg/L) 123456 Top0.4150.2380.3900.4100.6050.609 Bottom0.4300.2660.5670.5310.7070.716

19. One of the first things to do when analyzing data is to PLOT the data This is not a useful way to plot the data. There is not a clear distinction between bottom water and top water zinc—even though Bottom>Top at all 6 locations. TopBottom

20. A better way TopBottom Connect points in the same pair.

21. A better way Bottom=Top