Question

explain why the mean should not be found for a sample of zip codes. which measure of center should be used instead?

choose the correct answer below.

a. zip codes are quantitative data, but are at the ordinal level of measurement. since they cannot be added in a meaningful way, the mean cannot be found. the median should be used instead.
b. zip codes are quantitative data, but are at the ordinal level of measurement. since they cannot be added in a meaningful way, the mean cannot be found. the mode should be used instead.
c. even though they are numeric data, zip codes are qualitative since they do not measure or count anything. the mean cannot be found since adding zip codes would be meaningless. for qualitative data, the median is the only measure of center that can be found.
d. even though they are numeric data, zip codes are qualitative since they do not measure or count anything. the mean cannot be found since adding zip codes would be meaningless. for qualitative data, the mode is the only measure of center that can be found.

Explanation:

🆕 New Concept Discovered: Types of Data and Levels of Measurement
Categorizing data to choose correct statistics

Step 1: Analyze the nature of zip codes

Even though zip codes consist of numbers (for example, 90210), they do not measure or count any quantity. You cannot perform meaningful arithmetic on them. For instance, adding two zip codes together or finding their average (mean) does not yield a meaningful geographic location or value. Therefore, zip codes are classified as qualitative (categorical) data rather than quantitative data.

Step 2: Determine the appropriate measure of center

Because qualitative data represents categories or labels rather than numerical quantities:

• The mean cannot be calculated because addition is meaningless for these labels.
• The median cannot be calculated because there is no inherent numerical order to rank them.
• The mode (the most frequently occurring value) is the only measure of center that makes sense for qualitative data, as it simply identifies the most common category or label in the sample.

Step 3: Match with the given options

• A & B are incorrect because they classify zip codes as quantitative data.
• C is incorrect because it suggests the median is the only measure of center that can be found for qualitative data.
• D correctly states that zip codes are qualitative, adding them is meaningless, and the mode is the only measure of center that can be found.

Answer:

D. Even though they are numeric data, zip codes are qualitative since they do not measure or count anything. The mean cannot be found since adding zip codes would be meaningless. For qualitative data, the mode is the only measure of center that can be found.