Which of the following describes a continuous variable?
A- The number of items sold at a craft booth for one day
B- The number of apps downloaded from a website one day
C- The diameters of the tree trunks at an evergreen farm
D- The number of baskets made by a basketball player
E- The shoe sizes of all shoes on sale at a department store
The correct answer and explanation is :
The correct answer is C- The diameters of the tree trunks at an evergreen farm.
Explanation:
To understand why option C is the correct answer, we need to first distinguish between continuous and discrete variables.
- Discrete variables are countable. These variables represent counts or integers that cannot take on every possible value within a given range. They are typically counted in whole numbers and are finite. For example, the number of items sold (A), the number of apps downloaded (B), and the number of baskets made by a basketball player (D) are all discrete variables. You cannot have a fractional number of items or baskets, for instance.
- Continuous variables, on the other hand, can take on any value within a certain range and can be measured with great precision. These values are often represented by real numbers and can be fractional. For example, a variable like the diameter of tree trunks (C) can take any value within a specific range, including fractional values such as 3.5 cm or 4.75 cm. The measurement can vary continuously and is not limited to specific, discrete values.
In Option C, the diameters of the tree trunks are a continuous variable because they can be measured with precision to any degree. For instance, a tree trunk could have a diameter of 10.2 cm, 10.25 cm, or 10.258 cm, indicating that the measurements can take on an infinite number of values within a given range.
In contrast:
- Option A (number of items sold), B (number of apps downloaded), and D (number of baskets made) are discrete because they involve counts that can’t be divided into smaller, meaningful parts.
- Option E (shoe sizes) might seem continuous but it is actually discrete in practice because shoe sizes are given in specific values (e.g., 7, 7.5, 8) and don’t encompass every possible real number within a range.
Therefore, the diameters of tree trunks (C) are the best example of a continuous variable among the options given.