Question

The average of 8 numbers is 24. If two numbers 18 and 30 are removed, the average of the remaining numbers is:

• A. 22
• B. 23
• C. 24
• D. 25

Hint:

You can solve this instantly by checking the average of the removed items! The average of the two removed numbers is $\frac{18 + 30}{2} = \frac{48}{2} = 24$. Since the average of the elements leaving the group is exactly equal to the overall group average (24), their removal will have zero impact on the rest of the group. The remaining average stays 24!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
An average is the balanced value of a group of numbers, representing the total value divided evenly among the individual entities. When elements are extracted from a set, we calculate the new average by finding the remaining sum total of the values and dividing it by the updated headcount of elements left in the group.

Step 2: Key Formula or Approach:
1. $\text{Original Sum} = \text{Original Average} \times \text{Original Count}$ 2. $\text{Remaining Sum} = \text{Original Sum} - \text{Sum of Removed Numbers}$ 3. $\text{New Average} = \frac{\text{Remaining Sum}}{\text{Remaining Count}}$

Step 3: Detailed Explanation:
Let's find the values systematically: Initial State: There are 8 values whose collective average matches 24. $$\text{Original Sum} = 8 \times 24 = 192$$ Removal Step: Two specific numbers (18 and 30) are extracted out of the dataset. Let's calculate the combined value of these removed entries: $$\text{Removed Value} = 18 + 30 = 48$$ New State: Deduct this value from our initial total to see the remaining sum: $$\text{Remaining Sum} = 192 - 48 = 144$$ Since 2 numbers were completely removed from the initial pool of 8 numbers, the remaining headcount is: $$\text{Remaining Count} = 8 - 2 = 6$$ Now, calculate the revised group average by dividing the remaining sum by the updated headcount: $$\text{New Average} = \frac{144}{6} = 24$$

Step 4: Final Answer:
The average of the remaining numbers is 24.