Question

For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?

• A. I only
• B. II only
• C. I and II only
• D. II and III only
• E. None of the above

Hint:

To find the average of a set of numbers, either add them together and divide by the total number of numbers, or use operations that maintain this equivalence.

Answer 1

The Correct Option is B

Step 1: Analyze statement I.
Ordering the numbers from highest to lowest and selecting the middle number is equivalent to finding the median, not the average. Therefore, statement I is not equivalent to the average. Step 2: Analyze statement II.
Dividing each number by 3 and then adding the results is the same as adding the numbers together first and then dividing the sum by 3. This is equivalent to calculating the average. Hence, statement II is correct. Step 3: Analyze statement III.
Multiplying each number by 6 and then dividing the sum by 9 does not give the same result as dividing the sum by 3. This is not equivalent to finding the average, so statement III is incorrect. Conclusion:
Thus, only statement II is correct, and the correct answer is (B) II only.