Analyze the following arguments drawn from various corporate and public policy contexts. Pair each argument with the abstract description that most accurately identifies its specific error in reasoning regarding numbers and percentages.
- In 2015, independent coffee shops captured 12% of total national coffee sales. By 2025, their market share rose to 28%. Clearly, independent coffee shops sold a greater volume of coffee in 2025 than they did a decade earlier.Takes for granted that an expansion in a relative proportion necessitates an increase in an absolute quantity, failing to consider that the overall whole may have significantly contracted.
- During the summer months, the municipal pool recorded 150 instances of minor injuries, compared to just 30 instances at the local lake. Therefore, swimming at the municipal pool is inherently more dangerous than swimming at the local lake.Concludes that one activity is more dangerous than another based solely on a higher absolute number of incidents, without considering the relative frequency with which both activities are undertaken.
- According to a public health report, 85% of pedestrian accidents in the downtown district last year involved individuals crossing at designated crosswalks, whereas only 15% involved individuals crossing elsewhere. This demonstrates that using a designated crosswalk makes a pedestrian more likely to be struck by a vehicle.Infers a higher likelihood of an event occurring under certain conditions based on those conditions characterizing a high proportion of the total events, ignoring the relative prevalence of the conditions themselves in the overall population.
- Five years ago, the manufacturing division accounted for 40% of our company's total expenses. Today, it accounts for only 25%. This proves that the manufacturing division has successfully reduced its operating costs over the past five years.Assumes that a decrease in a component's share of an overall total reflects a reduction in its absolute amount, overlooking the possibility that the overall total itself grew substantially.
Answer
The coffee shop argument matches with the flaw of assuming an increased proportion entails an increased absolute quantity. The municipal pool argument matches with the flaw of relying on absolute incident numbers without comparing baseline frequencies. The crosswalk argument matches with the flaw of using a high proportion of total events to infer likelihood without considering the prevalence of the conditions. The manufacturing division argument matches with the flaw of assuming a decreased share reflects a reduction in absolute amount.
Each argument commits a distinct variation of the Percentages vs. Numbers flaw. By identifying the exact premise type (absolute number vs. percentage) and the specific conclusion type (absolute number vs. rate), each argument maps uniquely to its corresponding abstract flaw description.
Step-by-Step Solution
Key Concept
Identifying statistical reasoning errors where an argument conflates proportional shares (percentages) with actual sizes (absolute numbers), or vice versa, without providing necessary baseline context.