Prob-Stats-Teacher-Book.pdf

# Teaching tips consider assigning the student

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Teaching Tips ± Consider assigning the “Student Introduction” materials as reading homework before you begin working on the modules. This way, students will have a basic understanding about the motivation behind the modules. Then at the beginning of the first class period, you can begin by framing the scenario. As a class, brainstorm what data you might need in order to evaluate the risk and potential loss in the community. Students may come up with some of the following: ± Location, value and construction material of homes in Happy Shores ± Historical information about hurricanes in Happy Shores and the geographic region ± Historical insurance claims in the area due to hurricanes, along with historical claims in other areas ± Data about hurricane frequency in the U.S. ± There is no correct list of data. The idea is to brainstorm with students about what kind of data they could review. ± Define “Statistics”—a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. ± Look at historical data about hurricanes and tropical storms. ± It is much more important for students to understand the concept of standard deviation than the details of its computation. Stress the meaning of standard deviation as a measure of spread that gives us an indication of how data in a distribution vary from the mean. Discussion Questions Q1: What do the histogram and dot plot tell us about the distribution of hurricanes and tropical storms since 1932? (p. 9) A1: We can see that the basic shape of both distributions is unimodal and skewed to the right. There appears to be an outlier year in which there are 15 hurricanes and 28 tropical storms (although we cannot necessarily assume that this is the same year from the graphs alone—we have to look at the raw data). We can see that the number of hurricanes spans from 2 to 15, and the number of tropical storms spans from 4 to 28 (spread). It appears that the middle of the hurricane distribution is around 6 and the middle of the tropical storm distribution is around 10 (center).

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Page 7 MODULE 1 Q2: What do the histogram and dot plot NOT show that might be important? (p. 9) A2: The histogram and dot plot do not show the year. We cannot see the changes in the number of hurricanes over time. This information would allow us to see the trend of hurricane/storm occurrences over time. It may be useful to know if it appears that the propensity of storms is increasing or decreasing. We also cannot gauge the intensity of storms; perhaps hurricane frequency and severity are related. Q3: What if there was one year that had 30 hurricanes? How would this affect the median, mean, and standard deviation of the data? (p. 10) A3: This would not adversely affect the median of the data. Median is resistant to the effect of outliers. This is a very important property of the median. Even if the maximum value is one million, the median is still the middle data value. Mean and standard deviation,
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