1. Descriptive Statistics and Graphing

2. The Normal Distribution If the frequency (or number) of data points is plotted on the Y-axis, a bell-shaped curve may be produced. # Slow Fast Running Speed of People

3. Skewed Distribution (Not Normal) # Slow Fast Running Speed of People

4. Central Tendency Mean – average Median – middle value Mode – most common value

5. Disadvantages - Mean Influenced by outliers Example- Population estimates of waterfowl on seven lakes: 400 200 220 210 340 250 44,000 Mean = 6,517

6. Disadvantages - Median The central number may not be representative, particularly with small samples. Example: 0, 0, 1, 2, 480, 500

7. Range 100, 75, 50, 25, 0 52, 51, 50, 49, 48

8. Standard Deviation The standard deviation describes the “spread” of data points. It is useful if the data fit a normal distribution. # Slow Fast Running Speed of People

9. Calculating the Standard Deviation

10. 1) Calculate the mean

11. 2) Calculate deviation from the mean

12. 3) Square the deviations

13. 4) Sum the squared deviations

14. 5) Divide by n-1

15. 6) Take square root of variance

16. Normal Distribution 68% of the data points are within 1 standard deviation of the mean: = mean + or – S.D. In the previous example, this is 31 + or – 5.42 31+5.42 = 36.42 31-5.42 = 25.58 Therefore 68% of the data will fall between 25.58 and 36.42.

17. Normal Distribution Approximately 95% of the data points are within 2 standard deviations of the mean: = mean + or – 2 S.D. In the previous example, this is 31 + or – (2 X 5.42) 31 + (2*5.42) = 41.84 31 – (2*5.42) = 20.16. Therefore 95% of the data points fall between 20.16 and 41.84. Approximately 99% of the data points fall within three standard deviations of the mean.

18. Heart Rate (beats per minute) Speed (kilometers per hour) 11 12 13 14 15 16 17 Variables 165 160 155 150 145 140 135 130

19. Number of mammals in a 1.2 ha woodlot in Clinton County, NY Grey squirrel – 8 Red squirrels – 4 Chipmunks – 17 White-footed mice – 26 White-tailed deer – 2 Create a Graph Website: http://nces.ed.gov/nceskids/graphing/

20. Bar Graph - Mammals

21. pH of an a pond in Clinton County, NY on 5/11/05 1:00 AM – 5.2 3:00 AM – 5.1 5:00 AM – 5.1 7:00 AM – 6.0 9:00 AM – 6.6 11:00 AM – 6.9 1:00 PM – 7.0 3:00 PM – 7.0 5:00 PM – 6.6 7:00 PM – 5.9 9:00 PM – 5.3 11:00 PM – 5.2

22. Line Graph - pH

23. Number of bird species observed in 9 woodlots in January 2006 in Clinton County, NY Size of Woodlot (ha)# Bird Species 3.311 813 3.613 14 1.17 1114 7.412 6.614 812

24. Number of bird species observed in 9 woodlots in January 2006 in Clinton County, NY

27. Group 1 - Hormone Weight (grams) Group 2 – No Hormone Weight (grams) 12.58 138.5 128 8 137.5 1410.5 137 10.58.5 9.56.5 117 Statistical Testing Mean = 12.05 7.95

28. Conclusion P is the probability that the difference is due to chance. If p > 0.05, conclude that the difference is due to chance. If p < 0.05, conclude that the difference is real (not due to chance).

29. t-test http://faculty.clintoncc.suny.edu/faculty/Michael.Greg ory/files/shared%20files/Statistics/t-test.xls http://faculty.clintoncc.suny.edu/faculty/Michael.Greg ory/files/shared%20files/Statistics/t-test.xls