Logical Reasoning

PT152 · S4 · Q15 Commentator: The reported epidemic

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Commentator: The reported epidemic of childhood obesity in our country is a myth.

Conclusion

The supposed epidemic of childhood obesity is a myth.

Intermediate Conclusion

The proportion of children who are obese cannot have gone up much over the last 8 years.

Evidence

There was only a 1 pound increase in children's average weight over the last 8 years.

Evaluate

If we aren't mathematically inclined, then the structural features to go off of are these: Premise: talks about average going up a little Conclusion: says that proportion couldn't have gone up much

The mathematical flaw here is that the author is treating "average" too literally, and thinking that

But average is the net effect of everyone together. You can have a lot of different up/down movements that balance out to be neutral (or almost neutral, at +1 pound).

Pretend that 100 pounds is considered obese for a 3rd grader.

8 years ago, here are the weights of our ten 3rd grade students: 50, 70, 70, 80, 80, 80, 90, 90, 110

Average weight = 80, proportion who are obese = 10%

Here are the weights of ten 3rd grade students now: 50, 50, 50, 80, 80, 80, 110, 110, 110

Average weight = 80, proportion who are obese = 30%

For simplicity's sake, I didn't even both to change the average. This shows how an average might move very little, if at all, even though the proportion of kids who are obese is now three times as much as it was before.

There could be kids putting on a lot more weight (who go from non-obese to obese) while those weight gains are offset by other kids losing weight, which is why the average stays stable.

Goal

Find an argument saying .

15.

Which one of the following contains flawed reasoning most similar to the flawed reasoning contained in the argument above?

  1. The average summer temperature over

    Bad Premise / Conclusion Match

    Here, the conclusion is about average (average should be the premise), and the premise is about what people believe, when the other half of the argument is supposed to be a claim about proportion / ratio / fraction / percentage of a subset.

    1% picked this

  2. Correct

    The proportion of employees who

    Why this is right

    The conclusion is about proportion and the evidence is about average. Huzzah! Our same objection would apply here: it's possible that a much higher percentage of people now make very high salaries. If, simultaneously, a lot of people now make much lower salaries, those two effects will balance out and cause the average to increase only slightly.

    Skill tested: Parallel Flaw · how this choice captures the argument's function is the move to repeat next time.

    90% picked this

  3. The proportion of apartment buildings

    Bad Premise Match

    The conclusion is correctly about proportion, but the premise is supposed to be about average. Instead, it's about number. Also, the original argument was saying "since average barely moved, proportion barely moved". This one is saying "since there's a substantial number of new apartment building, there must be a substantial increase to the proportion".

    3% picked this

  4. The average weight of adults

    Reversed Premise / Conclusion

    Here, the conclusion is about average and the support is about proportion. The original argument had those two ingredients reversed.

    2% picked this

  5. The average price of a

    Reversed Premise / Conclusion

    Again, the conclusion is about average and the support is about proportion. The original argument had those two ingredients reversed.

    4% picked this

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