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.

5. 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?

6. Other considerations - - -

7. Assessment Statement
1.1.1 State that error bars are a graphical representation of the variability of data.
1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples.

8. Looking at these data sets what observations can you make?
Boys Scores
Girls Scores 60 98 62 42 68 88 70 92 63 38 65 56 95 58 64 50 89

9. Based on data, what do you think is the average boy score and girl’s score
Boys Scores
Girls Scores 60 98 62 42 68 88 70 92 63 38 65 56 95 58 64 50 89

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

11. Does the average for girls ’74%’ accurately describe how the typical girl did on this test? Why? Or Why not?
Boys Scores
Girls Scores 60 98 62 42 68 88 70 92 63 38 65 56 95 58 64 50 89
Average
63,8 74

12. Does the average for boys ’63
Does the average for boys ’63.8%’ accurately describe how the typical boy did on this test? Why? Or Why not?
Boys Scores
Girls Scores 60 98 62 42 68 88 70 92 63 38 65 56 95 58 64 50 89
Average
63,8 74

13. Boys Scores Girls Scores 60 98 62 42 68 88 70 92 63 38 65 56 95 58 64
Looking at the data what is range (lowest score & highest score) of data (scores) for both boys & girls?
Boys Scores
Girls Scores 60 98 62 42 68 88 70 92 63 38 65 56 95 58 64 50 89

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

15. The spread of data Averages do not tell us everything about a sample.
Data can be very uniform meaning all bunched around the mean, or data can be spread out a long way from the mean.
The statistic that measures this spread is called the standard deviation.

16. Standard Deviation
The standard deviation is a measure of the variation of the data.
For data that is evenly distributed each side of the mean (a normal distribution) 68% of the data lies within one standard deviation of the mean.

17. Formula for Standard Deviation
SD =
=square root
=sum (sigma)
X=score for each point in data _
X=mean of scores for the variable
n=sample size (number of observations or cases

19. Standard Deviation 68% of data falls within 1 standard deviation

20. Boys Scores Girls Scores 60 98 62 42 68 88 70 92 63 38 65 56 95 58 64
Based on the range of the data sets, which gender do you think would have a bigger Standard Deviation, boys or girls?
Boys Scores
Girls Scores 60 98 62 42 68 88 70 92 63 38 65 56 95 58 64 50 89

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

22. What would be the best way to graph this data in lab report
What would be the best way to graph this data in lab report? What things should your graph include?
Boys Scores
Girls Scores 60 98 62 42 68 88 70 92 63 38 65 56 95 58 64 50 89
Average
63,8 74
Standard Deviation
3,5
24,3

23. 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

24. 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

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

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

27. 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

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

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

30. 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

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

32. What non-overlapping error bars mean

33. YOUR Turn To PRACTICE.

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

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

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

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

38. 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?

39. Assessment Statement
1.1.1 State that error bars are a graphical representation of the variability of data.
1.1.4 Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples.