In Exercises 11 and 12, determine whether the data are qualita...

Question

In Exercises 11 and 12, determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set.

The six top-earning states in 2019 by median household income are listed. (Source: U.S. Census Bureau)

1. Maryland 2. New Jersey 3. Hawaii

4. Massachusetts 5. Connecticut 6. Alaska

Accepted Answer

Hello, everyone, let's take a look at this question together. A teacher records the final exam scores of students in a mathematics class. The scores are 85, 92, 76, 88, and 95. Are these data qualitative or quantitative, and what is the level of measurement? Is it answer choice A, qualitative and ordinal? Answer choice B, quantitative and ratio? Answer choice C, quantitative and interval, or answer choice D qualitative and nominal. So, in order to solve the question, we have to recall what we have learned about qualitative versus quantitative data, as well as the different levels of measurement to determine which type of data and level of measurement best describes the final exam scores of students in a mathematics class. And comparing qualitative versus quantitative data, we can recall that qualitative data describes categories or qualities. Whereas quantitative data involves numerical values that represent a measurable quantity, and looking at the data that we are provided, which are the final exam scores of students in a mathematics class, which are 85, 92, 76, 88, and 95, we can identify that the data are numerical scores, therefore, they are quantitative data. And since the data is quantitative, we can eliminate answer choice A and answer choice D as they both contain qualitative, which the data is not qualitative. And then for the level of measurement, we know there are 4 levels of measurement in statistics, starting with the nominal level of measurement, which involves categories with no inherent order. For example, hair color or gender. Then we have the ordinal level of measurement, which involves categories with a meaningful order, but unequal or unmeasurable intervals between them, such as letter grades or satisfaction ratings. Then we have the interval level of measurement, which involves numerical values with equal spacing, but no true zero, such as temperature in Celsius. And lastly, we have the ratio level of measurement, which involves numerical values with equal spacing, and a true zero, allowing for meaningful ratios, for example, height, weight, or age. And given that our data is the final exam scores of students in a mathematics class, we know that exam scores have a true zero, and the differences between the values are meaningful. Therefore, the level of measurement for the exam scores in the mathematics class is ratio, as the ratio level of measurement involves numerical values with equal spacing and a true zero, allowing for meaningful ratios. So the data are quantitative, and the level of measurement is ratio, making answer choice be the correct answer, and all other answer choices are incorrect. Have you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Qualitative vs. Quantitative Data

Levels of Measurement

Median Household Income

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