Question

When age is rounded to the nearest year, do the data stay continuous, or do they become discrete? Why?

Answer 1

Definitions:-

• If a data set is continuous, then the associated random variable could take on any value within the range.
• Discrete variables have distinct values.

Age is measured in units that, if precise enough, could be any number. Therefore the set they come from is infinite. For example, someone could be 22.32698457 years old or 22.32698459 years old. We could be infinitely accurate and use an infinite number of decimal places, therefore making age continuous.

However, in everyday appliances, all values under 6 years and above 5 years are called 5 years old. So we use age usually as a discrete variable.

The age of an individual in years could take on a finite number of values within our range. Age could be 9, or 42, or 75, but it couldn't be 75.5, for example. The data distribution for this random variable would be discrete.

Therefore when age is rounded to the nearest year, the data become discrete.