Which of the following statements correctly differentiates between continuous and categorical data?
The correct distinction between continuous and categorical data lies in their characteristics. Continuous data can take on an infinite number of values within a given range (such as height, weight, temperature) and is typically represented by numeric values. It can be measured and expressed with high precision. In contrast, categorical data is non-numeric and represents distinct categories or groups (such as gender, color, or product type). These categories can be nominal (no specific order, like color) or ordinal (with a defined order, like education level), but the defining trait is that they do not have the same range of values as continuous data. Option A (Continuous data is always numeric, while categorical data is always non-numeric) is partially true, but not all continuous data is numeric (e.g., continuous time data could be expressed in non-numeric units). Option B (Continuous data represents distinct groups, while categorical data represents measurable quantities) is incorrect because continuous data represents measurable quantities, not groups. Option D (Categorical data can only be ordinal, while continuous data is always nominal) is incorrect because categorical data can be both ordinal and nominal, while continuous data cannot be either. Option E (Continuous data is qualitative, while categorical data is quantitative) is incorrect because continuous data is quantitative, not qualitative.
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