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Descriptive Statistics and Graphing

0. Descriptive Statistics and Graphing. #. Slow Fast Running Speed of People. 0. The Normal Distribution. If the frequency (or number) of data points is plotted on the Y-axis, a bell-shaped curve may be produced. 0. Skewed Distribution (Not Normal). #.

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Descriptive Statistics and Graphing

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  1. 0 Descriptive Statistics and Graphing

  2. # Slow Fast Running Speed of People 0 The Normal Distribution • If the frequency (or number) of data points is plotted on the Y-axis, a bell-shaped curve may be produced.

  3. 0 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. 0 Range • 100, 75, 50, 25, 0 • 52, 51, 50, 49, 48

  8. # Slow Fast Running Speed of People 0 Standard Deviation • The standard deviation describes the “spread” of data points. It is useful if the data fit a normal distribution.

  9. 0 Calculating the Standard Deviation

  10. 0 1) Calculate the mean

  11. 0 2) Calculate deviation from the mean

  12. 0 3) Square the deviations

  13. 0 4) Sum the squared deviations

  14. 0 5) Divide by n-1

  15. 0 6) Take square root of variance

  16. 0 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 – 5.4231+5.42 = 36.4231-5.42 = 25.58 • Therefore 68% of the data will fall between 25.58 and 36.42.

  17. 0 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) = 41.8431 – (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. Variables 165 160 155 150 145 140 135 130 Heart Rate (beats per minute) 11 12 13 14 15 16 17 Speed (kilometers per hour)

  19. 0 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. 0 Bar Graph - Mammals

  21. 0 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. 0 Line Graph - pH

  23. 0 Number of bird species observed in 9 woodlots in January 2006 in Clinton County, NY

  24. 0 Number of bird species observed in 9 woodlots in January 2006 in Clinton County, NY

  25. 0 Number of bird species observed in 9 woodlots in January 2006 in Clinton County, NY

  26. 0 Number of bird species observed in 9 woodlots in January 2006 in Clinton County, NY

  27. Group 1 - HormoneWeight (grams) Group 2 – No HormoneWeight (grams) 12.5 8 13 8.5 12 8 12 8 13 7.5 14 10.5 13 7 10.5 8.5 9.5 6.5 11 7 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.Gregory/files/shared%20files/Statistics/t-test.xls

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