A continuous variable is a type of quantitative variable that can assume an infinite, uncountable number of values within a given range. The defining characteristic is that for any two values, it is always possible to find another value between them. For example, height, weight, and temperature are continuous because a measurement can be refined to greater and greater precision (e.g., 70.1 inches, 70.11 inches, 70.112 inches). Histograms are the appropriate visualization to understand the distribution of such variables by grouping the uncountable values into a finite number of bins.

A: "Never stops changing" is an informal and imprecise phrase that is not a standard statistical definition for a continuous variable.

B: This is the definition of a discrete variable, which has a finite or countably infinite set of distinct values (e.g., number of employees).

D: This describes a high-cardinality categorical variable. Continuous variables are quantitative (numeric), not categorical (labels or groups).

1. Databricks Documentation

Data visualization in Databricks: While not providing a formal definition

the documentation states that a histogram "plots the frequency distribution of a numeric column." This directly supports the use case in the question

where histograms are created for continuous (numeric) variables. (See: Databricks Documentation > Visualizations > Histogram).

2. PennState

STAT 200: Elementary Statistics Courseware: In Lesson 1.2

"Types of Variables

" a continuous variable is defined as "a quantitative variable that has an infinite number of possible values that are not countable." This directly supports option C.

3. MIT OpenCourseWare

18.05 Introduction to Probability and Statistics

Spring 2014: The class notes for "Topic 2: Discrete and Continuous Variables" define a continuous random variable as one whose set of possible values is an entire interval of numbers

which is an uncountable set. This aligns perfectly with the correct answer. (See: MIT OCW

18.05

Topic 2 Notes

Section 1).