Question

The mean of 10 numbers is 18. If one number is excluded, the mean becomes 17. What is the excluded number?

• A. 27
• B. 28
• C. 30
• D. 29

Hint:

To find the excluded number when the mean changes after removal, calculate total sum first, then subtract the new total sum from the old total sum.

Answer 1

The Correct Option is A

Step 1: Calculate the total sum of all 10 numbers using the mean: \[ \text{Sum of 10 numbers} = 10 \times 18 = 180. \] Step 2: Let the excluded number be \(x\). After excluding \(x\), the mean of remaining 9 numbers is 17, so \[ \text{Sum of remaining 9 numbers} = 9 \times 17 = 153. \] Step 3: The excluded number \(x\) is the difference between the total sum and sum of remaining numbers: \[ x = 180 - 153 = 27. \] Step 4: Check the options. The number 27 corresponds to option (A).