invest_3ed.pdf

# Chancerossman 2015 iscam iii investigation a 5 below

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Chance/Rossman, 2015 ISCAM III Investigation A 5 Below is a time plot of fatalities per 100,000 population using Wikipedia’s data from 1899 to 2013. (c) Write a few sentences summarizing how this new variable was calculated and what you learn from the time plot of these data. (d) In 1973 (before the speed limit was capped at 55 mph nationwide), the data report 25.507 fatalities per 100,000 people, compared to 21.134 in 1974 (after the national limit). Did the rate of fatalities decrease between these two years? If so, by how much? Does that appear to be a “large” difference? How are you deciding? Absolute differences , like you calculated in (d), can be difficult to evaluate , especially if you don’t consider the magnitude of values they come from. You might respond differently to a box of M&Ms coming up 4 candies short, than to a difference of 4 fatalities per 100,000 people (about 10,000 more deaths across the U.S. in one year). One way to take into account the magnitude of the data values you are comparing is to compute the percentage change : percentage change = (current rate previous rate) × 100% previous rate (e) Calculate and interpret this value. In particular, is this a positive or negative value; what does that imply?

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Chance/Rossman, 2015 ISCAM III Investigation A 6 Below is a time plot of the year-to-year percentage change, starting in 1900. (f) Why doesn’t this time plot start in 1899? (g) Write a few sentences describing what you learn from this graph. Are there any unusual features? Can you conjecture an explanation for any of these features? From this graph, we notice that there is variability in how these values change from year to year. Much of statistical investigation is measuring, accounting for, and trying to explain variability. In particular, we still can’t judge whether the percenta ge change you computed between 1973 and 1974 is particularly large until we compare it to the percentage changes for the other years. Below is a dotplot displaying the distribution of the percentage change values for this data set. (h) Explain what each dot represents. What information is revealed by this plot that was less clear in the time plot? How might you use this graph to measure how unusual the 1973/1974 percentage change is? What information is lost in this graph compared to the time plot?
Chance/Rossman, 2015 ISCAM III Investigation A 7 When looking at a distribution of a single variable like this, we are often interested in three key features: x Center: What would you consider a “typical” value in the distribution? x Variability: How clustered together or consistent are the observations? x Shape: Are some values more common than others? Are the values symmetric about the center? Are there any unusual observations that don’t follow the overall pattern? In describing these features, it is often helpful to summarize a characteristic with a single number. To summarize the center of the distribution, we often report the mean or the median . To summarize the variability of the distribution, we often report the standard deviation or the interquartile range . For now we will focus on the mean and standard deviation, a very common pairing.

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