Question

Classify the following as qualitative or quantitative statements, giving your reasons. (a) The sun is approximately 93 million mi from Earth. (b) Leonardo da Vinci was a better painter than Michelangelo. (c) Ice is less dense than water. (d) Butter tastes better than margarine. (e) A stitch in time saves nine.

Short answer

(a) Quantitative, (b) Qualitative, (c) Quantitative, (d) Qualitative, (e) Qualitative.

Step-by-step solution

Understanding Qualitative vs. Quantitative Statements

A qualitative statement describes qualities or characteristics that are not measurable, often including opinions or descriptions. A quantitative statement involves measurable quantities, often expressed numerically.

Analyze Statement (a)

Statement (a) 'The sun is approximately 93 million mi from Earth' provides a numerical distance measure, which is quantitative because it involves a specific, measurable number.

Analyze Statement (b)

Statement (b) 'Leonardo da Vinci was a better painter than Michelangelo' involves a subjective opinion about painting quality. This statement is qualitative as it lacks measurable data.

Analyze Statement (c)

Statement (c) 'Ice is less dense than water' describes a physical property that can be measured (density). Therefore, it is a quantitative statement because it relates to scientific measurement.

Analyze Statement (d)

Statement (d) 'Butter tastes better than margarine' is an opinion on taste, which is subjective and cannot be measured numerically, making it a qualitative statement.

Analyze Statement (e)

Statement (e) 'A stitch in time saves nine' is a proverb suggesting that timely actions prevent larger problems. As it relies on metaphorical language and lacks specific measures, it is qualitative.

Key concepts

Qualitative Statements

Qualitative statements are expressions that describe attributes, qualities, or characteristics without relying on numerical data. These statements often focus on the perception or opinion of the observer rather than measurable facts. For example, when someone says, "Leonardo da Vinci was a better painter than Michelangelo," it reflects a personal assessment of artistic style and skill rather than a fact that can be measured with statistics or experiments.
Qualitative statements can vary based on cultural, personal, or situational perspectives, making them subjective.

• Reflect personal opinions
• Cannot be measured with numbers
• Often include descriptive language

Quantitative Statements

Quantitative statements are characterized by their reliance on numerical data and measurable information. Such statements aim to present facts that can be quantified, utilizing numbers, statistics, or measurable parameters. A statement such as "The sun is approximately 93 million miles from Earth" represents a quantitative statement.
This is because it conveys a specific measure of distance that can be verified and universally understood due to its reliance on measurable data.

• Express numeric values
• Involve measurements
• Can be tested and verified

Measurable Quantities

Measurable quantities pertain to aspects that can be expressed in terms of numbers or amounts which allow for standard verification. These quantities often relate to physical and observable attributes, such as size, density, distance, or weight. In the statement, "Ice is less dense than water," density can be quantified in terms of mass per unit volume. This makes it a measurable quantity.

• Allow for objective measurement
• Have standard units of measure like meters, grams, etc.
• Enable comparison through precise calculation

Subjective Opinions

Subjective opinions are intrinsically linked with personal perspectives and feelings, serving as the foundation of many qualitative statements. They reflect individual interpretations rather than universal truths, which means they can vary widely between different people. An example of this would be, "Butter tastes better than margarine."
The statement is grounded in personal taste and preference, illustrating a subjective view rather than a measurable fact.

• Depend on personal perspectives
• Cannot be objectively measured
• Are influenced by individual experiences