Identify the data set’s level of measurement. number of milligrams of tar in 95 cigarettes A. interval B. ordinal C. nominal D. ratio
The correct answer and explanation is:
Correct Answer: D. Ratio
Explanation:
To identify the level of measurement of a data set, we need to consider what type of data is being measured and how that data can be meaningfully interpreted. The levels of measurement are nominal, ordinal, interval, and ratio, each with increasing mathematical meaning.
In this case, the data set refers to the number of milligrams of tar in 95 cigarettes, which is a quantitative measurement. Let’s break down the levels of measurement to see which one fits:
1. Nominal
- Definition: Categories without a specific order or numerical value (e.g., colors, names, brands).
- Example: Types of cigarette brands.
- Why Not Nominal? Milligrams of tar is numerical and measurable, not just a name or label.
2. Ordinal
- Definition: Categories with a specific order but unequal or unknown differences between them.
- Example: Ranking cigarettes as low, medium, or high in tar content.
- Why Not Ordinal? The data are exact measurements (milligrams), not ranks or levels.
3. Interval
- Definition: Numerical data with equal intervals between values but no true zero point (e.g., temperature in Celsius).
- Example: Time of day.
- Why Not Interval? The data have a meaningful zero point (0 mg means no tar), which interval data do not.
4. Ratio
- Definition: Numerical data with equal intervals and a true zero point, allowing for comparisons like “twice as much.”
- Example: Height, weight, age, and in this case, milligrams of tar.
- Why Ratio is Correct:
- The number of milligrams is numeric.
- There is a true zero point (0 mg = no tar).
- You can say one cigarette has twice as much tar as another.
Conclusion:
The number of milligrams of tar in 95 cigarettes is measured on a ratio level because it is a continuous numerical variable with a meaningful zero, and mathematical operations like multiplication and division make sense.