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 Question:
The concept of the arithmetic mean (or average) is the focus here. The mean is calculated by taking the sum of all observations and dividing it by the total count of those observations. When a value is removed from a set of data, both the total sum and the count of numbers change. By comparing the total sum of the original set with the total sum of the new set, we can isolate and identify the exact value of the number that was excluded. This is a classic "missing data" problem in statistics.
Step 2 : Key Formulas and approach:
The central formula used in this problem is: $$\text{Sum of observations} = \text{Mean} \times \text{Total number of items}$$ The approach follows these steps:
Calculate the total sum of the original 5 numbers.

Calculate the total sum of the remaining 4 numbers.

Subtract the new sum from the original sum to find the excluded value.

Step 3 : Detailed Explanation:

Step 1: Calculate the initial sum of the 5 numbers. Sum = $28 \times 5 = 140$.

Step 2: Calculate the sum of the 4 numbers after one is excluded. Sum = $25.5 \times 4 = 102$.

Step 3: Find the difference between the two sums to get the excluded number. $140 - 102 = 38$.

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