Match the following attributes of a city with the appropriate scale of measurements. Which one of the following combinations is correct?
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When working with scales of measurement, remember:
- Nominal scale: Used for labeling or categorizing variables.
- Ordinal scale: Used for ordered categories where the difference is not meaningful.
- Interval scale: Used for ordered variables with meaningful differences but no true zero point.
- Ratio scale: Used for variables with a true zero point, where both differences and ratios are meaningful.
We are asked to match each of the given attributes with the appropriate scale of measurement. Let’s evaluate each attribute and its correct scale:
Statement (P): "Average temperature (°C) of a city"
The average temperature is a measurement of a continuous quantity that can be placed on a scale where the difference between values is meaningful, but there is no true zero point. This is best described by the Interval scale (I), where differences between values are meaningful, but ratios are not. So, (P) matches with (I).
Statement (Q): "Name of a city"
The name of a city is a categorical variable and is used for labeling purposes only. The Nominal scale (III) is used for variables that categorize or name without a specific order or ranking. Thus, (Q) matches with (III).
Statement (R): "Population density of a city"
The population density is a ratio measurement because it has a true zero point (zero density means no population), and ratios of population densities make sense (e.g., one city having twice the population density of another). Therefore, (R) matches with (IV).
Statement (S): "Ranking of a city based on ease of business"
The ranking of a city is an ordinal scale because the cities are ordered based on their ease of doing business, but the exact difference between the ranks may not be the same. So, (S) matches with (II).
Conclusion:
The correct combination is (P)-(I), (Q)-(III), (R)-(IV), (S)-(II). Thus, the correct answer is (A).
