Question

The mean of 5 numbers is 28. If one number is excluded, the mean of the remaining 4 numbers becomes 25.5. The excluded number is:

• A. 35
• B. 38
• C. 37.5
• D. 40

Hint:

To multiply any multi-digit integer by 5 quickly in your head, cut the original number in half and multiply the result by 10 (or append a zero)! For instance: half of $28$ is $14 \rightarrow 140$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The arithmetic mean is equal to the total sum of all values divided by the count of observations. By computing the total sum before and after excluding a data point, the difference between the two totals yields the exact value of the excluded number.

Step 2: Key Formula or Approach:
$$\text{Sum of observations} = \text{Mean} \times \text{Total number of items}$$ $$\text{Excluded Number} = \text{Sum of original 5 numbers} - \text{Sum of remaining 4 numbers}$$

Step 3: Detailed Explanation:
1. Compute the initial total sum of the $5$ numbers: \[ \text{Sum}_{5} = 28 \times 5 = 140 \] 2. Compute the new sum of the remaining $4$ numbers using the value $25.5$ given in the prompt: \[ \text{Sum}_{4} = 25.5 \times 4 = 102 \] Subtracting the two sums gives the value of the removed number: \[ \text{Excluded Number} = 140 - 102 = 38 \]

Step 4: Final Answer:
The excluded number is 38.