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

Ask by Guerrero Craig. in the United Kingdom
Mar 18,2025

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Answer

Oliver is correct because shoe sizes are distinct and countable values, making them discrete data.

Solution

\( \textbf{Step 1: Identify the Given Data} \) 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. \( \boxed{\text{Oliver is correct because the shoe sizes are distinct and countable values, which is characteristic of discrete data.}} \)

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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.

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