Question

The mean of 12 numbers is 19. If 4 is subtracted from each number, then the new mean is

• A. 17
• B. 23
• C. 21
• D. 15

Answer 1

The Correct Option is D

Let the sum of the 12 numbers be \( S \). The mean is given by: \[ \text{Mean} = \frac{S}{12} \] We are given that the mean is 19, so: \[ \frac{S}{12} = 19 \quad \Rightarrow \quad S = 19 \times 12 = 228 \] Now, if 4 is subtracted from each number, the new sum of the numbers will be: \[ S' = S - 4 \times 12 = 228 - 48 = 180 \] The new mean is: \[ \text{New Mean} = \frac{S'}{12} = \frac{180}{12} = 15 \]

The correct option is (D): \(15\)