1. Ask statistical questions
Data Literacy Project
Mini-lesson 1:
Think statistically
and
Ask statistical questions

2. FISH
1. How long is this fish? cm

3. 2. How long are the fish in this river?

4. Min sea level pressure (mb)
HURRICANES
3. What was the maximum wind speed for hurricane Katrina?
Year
Seasonal order
Name
Duration days
Max wind speed (knots)
Min sea level pressure (mb)
Deaths
2005 12
Katrina 8
150
902
1833

5. 4. How would you describe the wind speed for the hurricanes in the 2005 hurricane season?

6. What is the EPA combined mileage rating for the 2011 Bugatti Veyron?
GAS MILEAGE
Background: The U.S. EPA rates every vehicle sold in the US for its gas mileage in city driving, on the open highway, and a combined city-highway rating. Ratings are in miles per gallon (mpg).
What is the EPA combined mileage rating for the 2011 Bugatti Veyron?
Make
Model
Year
Highway (mpg)
City (mpg)
Combined (mpg)
Bugatti
Veyron
2011 15 8 10
Answer:

7. 6. Based on the following sample, how variable is the EPA highway mileage rating for sport cars?
Make
Model
Year
City (mpg)
Highway (mpg)
Combined (mpg)
Bugatti
Veyron
2011 8 15 10
Audi
TT Roadster quattro 22 31 23
Honda
CR-Z 37 34
Mini-Cooper
Works 25 33 28
Mazda 3 29
Jaguar XJ 16 19

8. For each of the three situations (fish, hurricanes, and car mileages), how are the first and second questions different?
Which of the two questions provides the most insight into fish, hurricanes, and car mileages in general?
(Why?)

9. Three important ideas:
Scientists and engineers make observations and collect data with a question in mind.
They collect data from more than one example – from as many examples as is feasible. When measuring many examples, scientists and engineers expect that the data they collect will vary.
When answering their question, they have to come to understand why the data vary.
Variable because they are measuring more than one thing.

10. RESEARCH QUESTIONS What is the average age of the pennies in my jar?

11. What is the average age of the pennies in my jar?
How could we figure this out?

12. What is the average age of the pennies in my jar?
Answer with descriptive statistics
Average or Mean
Central tendency
Standard Deviation
Describes how much the age of the pennies vary around the mean

13. Mean
Example:
Mean Age:
SD: +/-12.1
1 - Standard Deviation

14. Challenge Can’t do every single penny – must sample
What problems do you foresee if we sample?

15. Challenge Can’t do every single penny – must sample
What problems do you foresee if we sample?
Sample must be representative of the population
Should be close to the mean and variation
How do we sample so that it is representative?

16. Challenge Can’t do every single penny – must sample
What problems do you foresee if we sample?
Sample must be representative of the population
Should be close to the mean and variation
If it is not – then we can’t be confident in our results
How do we sample so that it is representative?
Randomly vs biased samples?

17. Statistics Discussion
If we sample, we have to be careful that the way the samples are chosen will not result in bias so that our samples would not really reflect the population
“ A famous example is a political telephone survey conducted during the Truman-Dewey presidential race. Survey results indicated that Dewey would win by a landslide, failing to account for the fact that telephones were expensive at the time and only owned by a small, wealthy fraction of the population — people who tended to support Dewey more than the average voter.”

18. Challenge Can’t do every single penny – must sample
What problems do you foresee if we sample?
Sample must be representative of the population
Should be close to the mean and variation
If it is not – then we can’t be confident in our results
How do we sample so that it is representative?
Randomly vs biased samples?
Sample size?

19. Does sample size influence the “representativeness” of the sample
Look at graphs – age of people from the 2000 census drawn from a population of 5000 people
Does sample size influence “representativeness” of each trial?

20. Another way to look at the results:

21. Another way to look at the results

22. Some thoughts:
What sample size would you feel most confident that your data would be “representative” of the actual population?

23. Some thoughts:
What sample size would you feel most confident that your data would be “representative” of the actual population?
If you couldn’t afford 500 samples (because of time or money), what choice would you make from there?

24. Some thoughts:
What sample size would you feel most confident that your data would be “representative” of the actual population?
If you couldn’t afford 500 samples (because of time or money), what choice would you make from there?
What if you wanted to maximize your result while minimizing your sampling effort?

25. Major Points:
Sample size influences the potential that your sample is representative of the population
Larger sample size will be more likely to be representative of the population
Smaller sample size has a greater possibility of being biased away from the population
Sample of size of 30 is a good starting point

26. What is the average age of the pennies in my jar?
Which data would you trust more?
Sample Size 6
Sample Size 12
Sample Size 30
Mean Age
18.8
28.9
20.1
Standard Deviation
11.4
17.1
15.5

27. What is the average age of the pennies in my jar?
Which data would you trust more?
Actual Mean:
Actual Standard Deviation: 14.7
Sample Size 6
Sample Size 12
Sample Size 30
Mean Age
18.8
28.9
20.1
Standard Deviation
11.4
17.1
15.5

28. Some thoughts:
Even a small sample size could get it close some of the time

29. Some thoughts:
Even a small sample size could get it close some of the time
…but a larger sample size will get closer MORE of the time

30. How does this apply to you?
Are you conducting your study on every single individual in the population?
You are sampling
Sample should represent the population so that results can be generalized to the rest of the population
Too few samples – potentially biased

31. More Thoughts Your research question determines:
What descriptive statistics may be appropriate
What kind of data you should collect
How to communicate your data using tables or graphs
How to analyze your data using inferential statistics