Question

creating a two-way table

out of 106 total sophomores, there were forty-eight boys who received either an a, b, or c on their first math test. out of the twenty-eight total as, sixteen girls received as. out of the total fifty-four bs, thirty girls received bs. twelve boys received a c out of the twenty-four total cs on the test. which two-way table represents this information?

Explanation:

Extract given values

Using the Two-Way Frequency Tables knowledge point

• Total sophomores: \(106\)
• Total boys: \(48\)
• Total A's: \(28\)
• Girls with A's: \(16\)
• Total B's: \(54\)
• Girls with B's: \(30\)
• Boys with C's: \(12\)
• Total C's: \(24\)

Calculate remaining cell values

Using the Two-Way Frequency Tables knowledge point

• Boys with A's: \(\text{Total A's} - \text{Girls with A's} = 28 - 16 = 12\)
• Boys with B's: \(\text{Total B's} - \text{Girls with B's} = 54 - 30 = 24\)
• Girls with C's: \(\text{Total C's} - \text{Boys with C's} = 24 - 12 = 12\)
• Total girls: \(\text{Total sophomores} - \text{Total boys} = 106 - 48 = 58\)

Match with the options

Using the Two-Way Frequency Tables knowledge point

• Row "Boys": A = \(12\), B = \(24\), C = \(12\), Total = \(48\)
• Row "Girls": A = \(16\), B = \(30\), C = \(12\), Total = \(58\)
• Row "Total": A = \(28\), B = \(54\), C = \(24\), Total = \(106\)
• This matches the second table (middle option).

Answer:

• (A) First table (Boys Total = 106, Girls Total = 58, Total = 48)
• (B) Second table (Boys Total = 48, Girls Total = 58, Total = 106) (Correct answer)
• (C) Third table (Boys Total = 58, Girls Total = 48, Total = 106)