Investigation

Name1

First NameLast Name
Name2

First NameLast Name
E-mail
example@example.com
Work through this investigation with your partner. You should get in the habit of saving your responses at the bottom of each page. This will allow you to pick up where you left off if you don't finish in class or lose your connection etc.

Goals:
- Describe the distribution of a quantitative variable in terms of shape, center, variability, and unusual observations.
- Compare shapes between two distributions.
- Compare the centers between two distributions.
- Compare the variability between two distributions.
- Consider the appropriateness of different models of a data distribution.

Step 3: Explore the data

Distribution of number of hurricanes per year

Load the hurricane data into the "Descriptive Statistics" applet.

Press the Clear button to remove the example data.
Type AtlanticStorms.txt in the box and press the Use Data button to preview the data.
Press Use Data again to load the data in.
Use the Quantitative variable pull-down menu to select Hurricanes

You should see the dotplot we showed in class yesterday.
Let's think about the Mean

Check the Guess box for the Mean
Scroll to the right in the applet and Check the Show deviations from guessed mean box.
Scroll to the right more.
Move the red line for the location of the mean until the dotplot on the right "balances" (as best you can)
Now (scroll left) check the Actual box for the Mean.
Uncheck the Show deviations and Guess boxes.

(a) Report the value of the mean and provide a one-sentence interpretation based on the "balancing property" of the mean.

Key Ideas:

The mean is the value that balances the "deviations" so that the sum of the positive deviations equals the sum of the negative deviations. This is a very common measure of the center of the distribution.

The applet also tells you that the "sum of the absolute deviations" when using the mean is (minimized) around 356. If we divide this value by the number of observations, we get 356/173 = 2.06. This relates to the idea of standard deviation. If you check the Actual box for the standard deviation, you will find 2.603. We will interpret this value as a "typical deviation of an observation from the mean." Meaning, on average, roughly, the number of hurricanes in a year is 2.603 hurricanes from the average (some are closer, some are further, this is the average deviation). The standard deviation is therefore a useful measure of the spread of the distribution (at least for symmetric distributions).

You can also see a measure of skewness in the applet by checking the Actual box for Skewness. This value compares the distances above the mean to the distances below the mean. If the deviations tend to be larger to the right of the mean than to the left, the distribution is skewed to the right and the deviation statistic is positive.

For those who want formulas

(b) Back in the applet, use the pull-down menu to switch to the distribution of the number of major hurricanes (Make sure Guess Mean is unchecked). Comment (with numerical support) on how the center, spread, and variability of this distribution compares. ALSO comment on whether these differences make sense based on the variable change.

Modelling the distribution

The term model has lots of interpretations. For example, this website models hurricanes. The user specifies inputs such as sea surface temperature, moisture, and wind to explore how these factors impact the strength of a hurricane. This is useful for creating situations that haven't necessarily occured already, and allows us to make predications.

In this case, we want to model the long-run behavior of the distribution of the number of hurricanes. The blue graph below shows a possible identalized representation of the population of possible values for the number of hurricanes in a year.

In the One Variable applet

Specify the values of the mean and standard deviation from our dataset.

TAIQ: Would you say the "normal distribution" is a good model for our hurricane data? In other words, do the model and the observed data on the previous page behave the same way?

Use the pull-down menu to switch the population shape from Normal to Skewed Right.
Check the Show Sampling Options box.
Specify 173 as the Sample size
Press the Draw Samples button a few times.
(You can ignore the output to the right.)

You should see that the sample behaves like the model. But if you press Draw Samples again, there will be some variation and the samples won't exactly match the model.

(c) Which model seems more appropriate for our hurricane data?

NormalSkewed rightBothNeither
(d) Does our observed dataset seem like it could have come from the skewed right "population"? Explain your reasoning. (Does the behavior of the sample seem consistent with the "random variation" you saw in the samples you generated from the model?)
(e) According to the above model, we would see 14 OR MORE hurricanes in a year about .6% of the time. How often did such a total happen in our data set? Are these values similar?

Step 5: Formulate conclusions
(f) Would you consider it surprising to see 14 hurricanes in the Atlantic region in one year? Does this convince you that climate change is a problem? Justify your answers.
Step 6: Look back and ahead
(g) If you were to continue this investigation, what would you do next? (e.g., look at the data a different way, collect different data?)
Next Steps: Press the Review Answers button. You will have an opportunity to review your answers and then press Submit. After you finish submitting, a pdf file (attachment) will be sent to the email address given above. To submit that file:

- Both of you need to join an "investigation 0" group in Canvas : Follow the People link in Canvas and then find and select (the same) empty group.

- Then upload the pdf file (only one of you needs to submit)

Thanks!

For those who want formulas
Should be Empty:

Step 3: Explore the data

Modelling the distribution

Step 5: Formulate conclusions

Step 6: Look back and ahead