A shop sells shoes in the following standard sizes: \[ \begin{array}{c}3,3.5,4,4.5 \text { and } 5 . \\ \text { Oliver says "I think shoe size is discrete } \\ \text { data." } \\ \text { Trina says "I think shoe size is } \\ \text { continuous data." } \\ \text { Who is correct? } \\ \text { Give a reason for your answer. }\end{array} \text { } \quad \text { ? } \]

\( \textbf{Step 1: Identify the Given Data} \) The listed shoe sizes are: \[ 3,\quad 3.5,\quad 4,\quad 4.5,\quad 5. \] \( \textbf{Step 2: Understand the Definition of Discrete Data} \) Discrete data consists of distinct, separate values that can be counted. The numbers in the list represent individual, separate categories. \( \textbf{Step 3: Understand the Definition of Continuous Data} \) Continuous data can take any value within a given range and is typically measured, not counted. For example, the exact length of a foot could be any real number, but shoe sizes are provided in distinct increments. \( \textbf{Step 4: Apply the Definitions to the Shoe Sizes} \) Although the true measurement of a foot is continuous, the shoe sizes provided by the shop are a finite set of values. They do not include every possible number between, say, \(3\) and \(5\), but only the specified discrete sizes. \( \textbf{Step 5: Conclusion} \) Since the shoe sizes are provided as distinct values \( (3, 3.5, 4, 4.5, 5) \), they are discrete data. Therefore, Oliver is correct. \( \boxed{\text{Oliver is correct because the shoe sizes are distinct and countable values, which is characteristic of discrete data.}} \)