Question

For each of the following characteristics, indicate whether it would be considered a discontinuous characteristic or a quantitative characteristic. Briefly justify your answer.

1) Discontinuous characteristic
2) Quantitative characteristic

Answer 1

Discontinuous characteristics are categorical with no intermediate states, like blood type, while quantitative characteristics can be measured on a continuum, like height or weight. Quantitative can be further divided into discrete, counted in whole numbers, and continuous, measured in precise units including fractions.

Step-by-step explanation:

Discontinuous characteristics refer to traits that exist in distinct categories with no intermediate states, such as blood type or flower color in Mendelian genetics. On the other hand, quantitative characteristics are traits that can be measured and exist on a continuum, such as height or weight, often showing a range of variation.

Here is a list of the given characteristics and a justification of their type:

1. The number of pairs of shoes you own: Quantitative Discrete - You count shoes in whole numbers.
2. The type of car you drive: Qualitative - This is a category, not a measurement.
3. The distance from your home to the nearest grocery store: Quantitative Continuous - Distance can be measured in fractions and decimals.
4. The number of classes you take per school year: Quantitative Discrete - Classes are counted in whole numbers.
5. The type of calculator you use: Qualitative - Another categorical characteristic.
6. Weights of sumo wrestlers: Quantitative Continuous - Weight is measurable and can include fractions and decimals.
7. Number of correct answers on a quiz: Quantitative Discrete - Answers are counted in whole numbers.
8. IQ scores: Quantitative Continuous - Although scored in whole numbers, IQ is treated as continuous since it represents an underlying continuum of intellectual capability.

The number of times per week (e.g., visits to a park) is Quantitative Discrete data since you count the number of times in whole numbers. The duration, or amount of time, is Quantitative Continuous data because time can be measured down to infinitely small units. Colors of houses would be Qualitative data, based on categories rather than measurements.