I've passed eight university math courses and am working on my ninth. If you don't know much about math or cannot understand the calculations at the bottom of this post, please do not participate in this discussion.
What the JD Powers and Consumer Reports numbers say:
WESTLAKE VILLAGE, Calif.: 29 June 2005 — The automotive industry records an impressive 12 percent improvement in long-term vehicle quality, according to the J.D. Power and Associates 2005 Vehicle Dependability Study (VDS) released today.
The study, which measures problems experienced by original owners of 3-year-old (2002 model-year) vehicles, provides useful information to both consumers and the automotive industry on long-term vehicle quality. For consumers, the VDS offers insight into the reliability and dependability of brands and specific models as they approach the end of a typical warranty period.
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JD Powers reports that 3-year-old (2002 model-year) Volkswagens have 335 problems per 100 cars. It also shows that Nissans have 275 problems per 100 cars, Mazdas have 252 problems per 100 cars and that Toyotas have 194 problems per 100 cars. This means that one single 3-year-old Volkswagen will have, on average, 335/100 = 3.35 problems. It also means that one single 3-year-old Nissan will have, on average, 2.75 problems and one single 3-year-old Mazda will have, on average, 2.52 problems and finally one Toyota will have, on average, 1.94 problems. This shows (see my math explanation below) that a 3-year-old Volkswagen will have, on average, only 3.35 - 2.75 = 0.6 (i.e., six tenths of one problem) more problems than a 3-year-old Nissan. Similarly it shows that a 3-year-old VW will have, on average, 3.35 - 2.52 = 0.83 more problems than a 3-year-old Mazda and 3.35 - 1.94 = 1.41 more problems than a 3-year-old Toyota.
All the over-the-top hyperbole about how unreliable VWs are is not borne out by the numbers for if you argue that 3-year-old VWs with an average of 3.35 problems per car are so unreliable, then you must also argue that 3-year-old Nissans, with an average of just six tenths fewer problems per car, are also extremely unreliable. I have never heard this level of hype regarding Nissan’s reliability problems nor have I heard it concerning Mazda’s reliability problems.
The JD Powers and Consumer Reports numbers do not show how the problems are distributed over the 100 cars of each group so you cannot assume that you know how they are distributed. We are also not given enough information to calculate the median, mode or standard deviation of the data set but as pointed out above we can calculate the average number of problems per car and hence the average difference in problems between two cars and as my calculations show the difference is less than 1.5 problems between a 3-year-old Toyota and a 3-year-old VW.
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Calculations:
Suppose we have one group of cars containing three European cars and another group containing three Asian cars. Let E1 be the number of problems the first European car has and let E2 be the number of problems the second European car has and let E3 be the number of problems that the third European car has. Similarly let A1, A2 and A3 be the number of problems for the three Asian cars.
So the total number of problems for the group of European cars would be E1 + E2 + E3 and the average number of problems per European car would be (E1 + E2 + E3) / 3. Similarly, the total number of problems for the group of Asian cars would be A1 + A2 + A3 and the average number of problems per Asian car would be (A1 + A2 + A3 ) / 3.
This information would seem to indicate that a European car would have, on average,
* (E1 + E2 + E3) / 3 - (A1 + A2 + A3 ) / 3
more problems than an Asian car. Let’s check it by directly calculating the average difference in problems between one European car and one Asian car by looking at every possible pairing of one European car with one Asian car and calculating the difference in problems for each of those possible pairings. If you then add up those differences in problems and divide by the number of possible pairings, you get the average difference in problems between a European car and an Asian car.
There are 9 possible unique pairings of one European car with one Asian car from our two groups of cars. The difference in problems for each of these 9 possible pairings are:
E1 - A1
E1 - A2
E1 - A3
E2 - A1
E2 - A2
E2 - A3
E3 - A1
E3 - A2
E3 - A3
If you add them up and divide by 9, we should get the same average calculated above. Let’s try it.
(3E1 + 3E2 + 3E3 - 3A1 - 3A2 - 3A3) / 9 = (E1 + E2 + E3 - A1 - A2 - A3) / 3 =
* (E1 + E2 + E3) / 3 - (A1 + A2 + A3) / 3
which is indeed the same as the average calculated above.
This method can be generalized to a group of N European cars and a group of N Asian cars. The April, 2006 Consumer Reports Auto issue said that there were 97 problems per 100 European cars and 44 problems per 100 Asian cars and using the method here we can see that that means a European car will have, on average, 97/100 - 44/100 = 0.53 more problems than an Asian car.
