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

Oliver is correct! Shoe sizes, particularly when they are measured in standard increments like 3, 3.5, 4, 4.5, and 5, represent discrete data. This is because they consist of distinct, separate values that cannot be divided into smaller increments within that set without creating new sizes. In real-world applications, understanding shoe sizes as discrete data helps both manufacturers and consumers manage sizing more effectively. For example, shoe brands often create charts to guide buyers in selecting their sizes based on foot measurements. This discrete categorization is crucial for ensuring a proper fit and reducing the likelihood of returns due to sizing issues.