Question

If 7 is the mean of 5, 3, 0.5, 4.5, \( a \), 8.5, 9.5, then the value of \( a \) is:

• A. 49
• B. 18
• C. 31
• D. 12

Hint:

To find the unknown in a mean problem, set up an equation based on the definition of mean: \(\text{Mean} = \frac{\text{Sum of elements}}{\text{Number of elements}}\).

Answer 1

The Correct Option is D

The mean of a set of numbers is given by: \[ \text{Mean} = \frac{\text{Sum of all elements}}{\text{Number of elements}} \] The given numbers are \( 5, 3, 0.5, 4.5, a, 8.5, 9.5 \), and the mean is 7. Therefore: \[ 7 = \frac{5 + 3 + 0.5 + 4.5 + a + 8.5 + 9.5}{7} \] Simplifying the numerator: \[ 7 = \frac{31 + a}{7} \] Multiplying both sides by 7: \[ 49 = 31 + a \] Solving for \( a \): \[ a = 49 - 31 = 18 \] Therefore, the correct answer is 12.