1. Understanding Numerical Data

2. Statistics Statistics is a tool used to answer general questions on the basis of a limited amount of specific data. Statistics allows us to make decisions about a population based on a sample of that population rather than on the entire population.

3. Why do we need Statistics? Let’s say that you want to know the lipid content of a typical corn grain. You could analyze one grain, but how would you know that you’d picked a “typical” grain? You’d get a better estimate of “typical” if you increased you sample size to a few hundred grain, or even to 10,000. Or to 1,000,000. Better yet….The only way to be certain your conclusions would be to measure all of the corn grains in the world. Since this is clearly impossible, you must choose grains that represent all of the grains in the world – that is, you must be working with a representative sample.

4. Statistics Terms Mean- The mean is the arithmetic average of a group of measurements. Median- The median is the middle value of a group of measurements.

5. Look at the below data set which number is the median. 12 21 15 17 18 20 24

6. Now describe how you would calculate the average of this data set. 12 21 15 17 18 20 24

7. Scientists often base answers to investigative questions on averages Thus in the earlier investigative question about the lipid content of a typical corn grain, if you took a sample of 10,000 corn, measured their lipid content, then calculated their average(mean) lipid content, would that average (mean) be an adequate description the lipid content of all corn in the world? Why? Or why not?

8. Other considerations - - -

9. Looking at these data sets what observations can you make? Boys ScoresGirls Scores 6098 6242 6888 7092 6338 6556 6595 5892 6450 6389

10. Based on data, what do you think is the average boy score and girl ’ s score Boys ScoresGirls Scores 6098 6242 6888 7092 6338 6556 6595 5892 6450 6389

11. Average Score Boys – 64% Girls – 74% Does this mean that girls did significantly better on the test?

12. Does the average for girls ’74%’ accurately describe how the typical girl did on this test? Why? Or Why not? Boys ScoresGirls Scores 6098 6242 6888 7092 6338 6556 6595 5892 6450 6389 Average63,874

13. Does the average for boys ’63.8%’ accurately describe how the typical boy did on this test? Why? Or Why not? Boys ScoresGirls Scores 6098 6242 6888 7092 6338 6556 6595 5892 6450 6389 Average63,874

14. Looking at the data what is range (lowest score & highest score) of data (scores) for both boys & girls? Boys ScoresGirls Scores 6098 6242 6888 7092 6338 6556 6595 5892 6450 6389

15. Standard Deviation Show the average difference each data point has from the mean. Shows how big the range of a data set is.

17. Based on the range of the data sets, which gender do you think would have a bigger Standard Deviation, boys or girls? Boys ScoresGirls Scores 6098 6242 6888 7092 6338 6556 6595 5892 6450 6389

18. Standard Deviation Boys – 3.4 Girls – 24.3 What does this difference in standard deviation mean?

19. What would be the best way to graph this data in lab report? What things should your graph include? Boys ScoresGirls Scores 6098 6242 6888 7092 6338 6556 6595 5892 6450 6389 Average63,874 Standard Deviation 3,524,3

20. Based on this graph what can you conclude, about the difference between how boys and girls did on this test? Error bars represent the standard deviation of the data sets

21. Data Analysis Conclusions things to think about: BIG vs. SMALL -- ERROR BARS Big error bars means lots of variation in data & data is less reliable to draw conclusions from Small error bars means less variation in data & data is more reliable to draw conclusion from

22. Big error bars = large standard deviation = BIG Range in data Small error bars = small standard deviation = small range in data

23. BIG vs. SMALL Error Bars Error bars represent the standard deviation of the data sets

24. Data Analysis Conclusions things to think about: OVERLAPPING ERROR BARS – When the values of error bars overlap on a graph it means that there is NOT a significant difference in averages and data sets. Error bars represent the standard deviation of the data sets

25. What overlapping error bars mean with respect to average data between

26. Overlapping Error Bars Error bars represent the standard deviation of the data sets

27. Data Analysis Conclusions things to think about: NON- OVERLAPPING ERROR BARS – When the values of error bars DO NOT overlap on a graph it means that there MAY BE a significant difference in averages and data sets. – In order to prove that there is a difference between this data set you must do a t test – t- tests test the differences between means. Error bars represent the standard deviation of the data sets

28. NON OVERLAPPING ERROR BARS Error bars represent the standard deviation of the data sets

29. What non-overlapping error bars mean

30. YOUR Turn To PRACTICE.

31. For condition A is there a significant difference between the control group & experiment group? Why or Why not?

32. For condition B, is there a significant difference between the control group & experiment group? Why or Why not?

33. For condition C, is there a significant difference between the control group & experiment group? Why or Why not?

34. Which data set (type of food) seems to be the most reliable and why?

35. Between which type of food does there seem to be a significant difference in the growth of fish? and explain why you made that conclusion?