Alice, Bob, and Cindy each drive about 1000 miles per month. Alice drives a truck which gets 10 mpg. Bob drives a 20 mpg car. Cindy drives a smaller vehicle which averages 40 mpg. The goal is to find the 3 friend's "average" mpg... Computing the regular arithmetic mean of the 3 mpg will lead to an incorrect average. Instead, there are two alternatives. One, invert each mpg to get gpm then compute the arithmetic mean, then re-invert back to mpg [this method is called a Harmonic Mean). Two, find the total number of miles driven and the total number of gallons used, then divide. Execute one or both of these methods and compare/contrast to the incorrect arithmetic mean. The three friends plan to buy newer, more efficient vehicles. Alice's new truck will get 13mpg. Bob is upgrading to a 28mpg car. Cindy is looking at a 55mpg hybrid. Who will save more gasoline with these upgrades? What upgraded mpg would the other two have needed in order to save the same amount? Again, there are two ways to find the answers. One, compare the gpm for each person's new car to their old car. Then find out how many gpm are saved by each person. Finally, take the largest saved gpm and apply that savings to the other two before inverting back. Two, compare the gallons used for each person's new car to their old car (each month). Then take the largest saved number of gallons and apply to the other two. Execute one or both of these methods and summarize!

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

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