Question

If the numbers 10, 8, 5, 7, \( x \), and 4 have an arithmetic mean of 8, then the value of \( x \) will be:

• A. 10
• B. 13
• C. 14
• D. 15

Hint:

To find the unknown term in a set of numbers when the arithmetic mean is known, use the formula for A.M. and solve for the unknown.

Answer 1

The Correct Option is C

The arithmetic mean (A.M.) of \( n \) numbers is given by the formula: \[ \text{A.M.} = \frac{\text{Sum of terms}}{n} \] In this case, we are given 6 numbers: 10, 8, 5, 7, \( x \), and 4, and the mean is 8. So, we have: \[ \frac{10 + 8 + 5 + 7 + x + 4}{6} = 8 \] Simplifying the sum of the known numbers: \[ \frac{34 + x}{6} = 8 \] Now, multiply both sides by 6: \[ 34 + x = 48 \] Solve for \( x \): \[ x = 48 - 34 = 14 \]