1. Statistics in Biology

4. The Mean
Mean (x̄) is a measure of the central tendency of a set of data. (average) Ex. Calculate the mean. Answer = 11.6

5. The Mean
Graphing the Mean  Bar Graph

6. Measures of Variability
Range: difference between largest/smallest values in data set Standard deviation (s) is a measure of the spread of most of the data

8. Standard Deviation

9. Standard Deviation
68% of all data fall within ± 1 standard deviation of the mean 95% of all data fall within ± 2 standard deviation of the mean 99.7% of all data fall within ± 3 standard deviation of the mean

10. Standard Deviation

11. Standard Deviation

12. Standard Deviation

13. Standard Deviation

14. Standard Deviation

15. Calculating Standard Deviation
Calculate the mean
Determine the differences
Square the differences
Sum the Squares
Divide by sample size (n) – 1
Take the square root

16. Measurements of Confidence
Uncertainty: the margin of error in a measurement Ex: digital scale: 126.4g (±0.1g)

17. Standard Error of the Mean
Standard Error of the Mean (SE or SEM): measures how close the sample mean is to the population mean
Measure of accuracy (if the true mean is known)
Measure of precision (if the true mean is not known)
The greater the sample size, the less the uncertainty in the calculations

18. Standard Error (SE or SEM)

19. Standard Error

20. Standard Error 95% confidence interval (95% CI):
95% confident that the true means falls between 2 SE above/below calculated mean
Graph with error bars Graph with error bars representing
representing SE of the mean % confidence interval

21. Error Bars

22. Error Bars

23. Error Bars Look for overlap of error lines If overlap-
difference is NOT significant
If no overlap-
difference IS significant

24. Error Bars Significance of Data
Which graph shows two means that are significantly different?
Hint: Look for the non-overlapping error bars.
Answer: The means in (c) are statistically different.

25. Error Bars Statements Fish2Whale food caused the most growth
Fish2Whale food caused more fish growth than did Budget Fude

26. Error Bars
Statements
More males in all four regions exhibited the trait measured than did females
More males in region 3 exhibited the trait measure than did females

27. The End