Descriptive Statistics and Graphing

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

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

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

Disadvantages - Mean Influenced by outliers Example- Population estimates of waterfowl on seven lakes: ,000 Mean = 6,517

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

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

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

Calculating the Standard Deviation

1) Calculate the mean

2) Calculate deviation from the mean

3) Square the deviations

4) Sum the squared deviations

5) Divide by n-1

6) Take square root of variance

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 – = = Therefore 68% of the data will fall between and

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) = – (2*5.42) = Therefore 95% of the data points fall between and Approximately 99% of the data points fall within three standard deviations of the mean.

Heart Rate (beats per minute) Speed (kilometers per hour) Variables

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:

Bar Graph - Mammals

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 – :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 – :00 PM – 5.2

Line Graph - pH

Number of bird species observed in 9 woodlots in January 2006 in Clinton County, NY Size of Woodlot (ha)# Bird Species

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

Group 1 - Hormone Weight (grams) Group 2 – No Hormone Weight (grams) Statistical Testing Mean =

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).

t-test ory/files/shared%20files/Statistics/t-test.xls ory/files/shared%20files/Statistics/t-test.xls