Question

Sample Set A has 25 data points with an arithmetic mean of 50. Sample Set B has 75 data points with an arithmetic mean of 100. Quantity A: The arithmetic mean of the 100 data points encompassing A and B. Quantity B: 80

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

When combining averages, always use weighted sums, not just the average of averages.

Answer 1

The Correct Option is B

Step 1: Total of Set A.
\(25 \times 50 = 1250\).
Step 2: Total of Set B.
\(75 \times 100 = 7500\).
Step 3: Combined total and mean.
Total = \(1250 + 7500 = 8750\).
Mean = \(\frac{8750}{100} = 87.5\).
Step 4: Compare with Quantity B.
87.5 vs 80. Quantity A is greater. Correction: The actual correct option should be (A) not (B).
Final Answer: \[ \boxed{\text{Quantity A is greater.}} \]