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Chapter 1: Problem 35

A New York Times editorial criticized a chart caption that described a dental rinse as one that "reduces plaque on teeth by over \(300 \%\)." What is wrong with this statement?

Short Answer

Expert verified
It is impossible to reduce plaque by more than 100%.

Step by step solution

01

Understand the Claim

The statement says that the dental rinse reduces plaque on teeth by over 300%. This implies a reduction greater than the initial amount of plaque present.
02

Analyze Percentage Reduction

A reduction of 100% means eliminating all of the plaque. Thus, a 100% reduction removes 100% of the original plaque amount, leaving no plaque.
03

Consider Exceeding 100%

Any percentage exceeding 100% in the context of reduction is logically flawed because you cannot remove more than the total amount of plaque present (i.e., you cannot eliminate more than 100% of the original plaque).
04

Re-evaluate the Statement

If reducing plaque by over 300% were possible, it would mean removing three times the amount of plaque that was originally present, which is impossible.
05

Conclude the Error

The error in the statement is that it suggests a reduction greater than 100%, which is an impossibility in the context of reducing something.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percentage error
Percentage error plays a crucial role when analyzing data claims. It's the quantitative difference between a measured or estimated value and the true value. Calculating this helps identify discrepancies in data presentation. In the given exercise about the dental rinse, the critical error is the misrepresentation of percentage reduction. Claiming a reduction greater than 100% is illogical because you cannot remove more plaque than there originally was. The correct maximum is a 100% reduction, signifying complete elimination.
logical analysis
Logical analysis helps identify errors in data interpretation and presentation. In this case, understanding that reducing plaque by over 300% defies logic is vital. A 100% reduction means no plaque remains. Anything more indicates a misunderstanding of percentage concepts. For students, building logical reasoning skills assists in accurately interpreting claims and spotting errors. Regular practice with real-world examples helps consolidate these skills.
  • Check if the claimed percentage makes sense.
  • Question if exceeding certain limits is possible.
Logical analysis acts as a filter for erroneous statements.
interpretation of data
Interpreting data accurately is essential. Misinterpreting results can lead to false conclusions and poor decisions. The editorial's criticism of the dental rinse ad highlights the importance of understanding data. Learning to interpret percentage reduction means recognizing the impossibility of reducing something by more than its total amount. An accurate interpretation would rephrase the claim to a realistic percentage, ensuring no miscommunication. Students should practice scrutinizing data presentations, examining if they make sense logically and quantitatively.

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