- A conditional relative frequency table requires rows or columns to sum to 1.0.
- Table 1 is a joint relative frequency table where rows and columns sum to 0.5.
- Table 2 shows row-conditional relative frequencies where each row (C and D) sums to 1.0.
- Table 3 is incomplete, making Table 2 the correct choice.
- Final Answer: \(\boxed{Table 2}\)
Explanation
- Analyzing the properties of conditional relative frequency tables
A conditional relative frequency table shows the proportion of data points falling into categories, given a condition. For a table to be row-conditional, each row must represent a specific category of the conditioning variable, and the entries within each row must sum to 1.0. Similarly, for a table to be column-conditional, each column must represent a category, and the entries in each column must sum to 1.0.
In the provided tables, we are looking for this property. Let's examine each:
- Table 1: Each row sum is \(0.25 + 0.25 = 0.50\), and each column sum is \(0.50\). This is a joint relative frequency table, not a conditional one, because the categories do not sum to 1.0 within their respective conditioning groups.
- Table 2: Row C has \(0.25 + 0.75 = 1.0\), and Row D has \(0.35 + 0.65 = 1.0\). Since each row sums to 1.0, this represents a row-conditional relative frequency table where categories C and D define the conditions.
- Table 3: While the row sums to 1.0 (\(0.75 + 0.25 = 1.0\)), it only provides data for one category (C). A conditional relative frequency table must include all categories of the conditioning variable (both C and D) to be a valid representation.
- Identifying the correct table
Based on our analysis, only Table 2 consistently satisfies the condition that each row sums to 1.0, representing the row-conditional relative frequencies for all categories (C and D). Therefore, Table 2 is the correct representation of a conditional relative frequency table.
Examples
In market research, you might want to compare the preferences of two different demographic groups (e.g., age groups C and D) for two different products (A and B). A row-conditional table allows you to see the percentage of people in each age group who prefer each product. For example, knowing that 75% of group C prefers product B (\(0.75\)) helps businesses tailor their advertising to specific audiences based on their conditional preferences.