Which of the following statement DOES NOT describe a continuous random variable? A. Height of students in a certain class B. The average weight of chicken each day C. The number of towns belong to Quezon Province D. The distance travelled by a delivery van in an hour
The correct answer and explanation is :
The correct answer is C. The number of towns belonging to Quezon Province.
Explanation:
A continuous random variable can take any value within a given range. Its possible values are uncountable and often represent measurements, like height, weight, distance, or time. These variables can be decimal numbers and have infinite possibilities within an interval.
Let’s examine each option:
- A. Height of students in a certain class
- Height is a measurement that can be expressed in fractions or decimals (e.g., 152.4 cm). It varies continuously without gaps between values, so it is a continuous random variable.
- B. The average weight of chicken each day
- Average weight is also a measurement that can have decimal values (e.g., 1.75 kg). Since it can vary continuously, this too is a continuous random variable.
- C. The number of towns belonging to Quezon Province
- This involves counting distinct items — the towns. You cannot have a fraction of a town (e.g., 21.5 towns does not make sense). The number of towns is whole and countable, making this a discrete random variable, not continuous.
- D. The distance travelled by a delivery van in an hour
- Distance is a measurement that can vary continuously (e.g., 45.7 kilometers). It can take on any value within a range and thus is a continuous random variable.
In short, continuous random variables deal with measurements and are infinitely possible within an interval. Discrete random variables, like the number of towns, involve counting distinct, separate outcomes. Therefore, option C does not describe a continuous random variable.