Question

If the mean of the numbers $7, 8, x, 11, 14$ is $x$, then the value of $x$ is:

• A. $9$
• B. $10$
• C. $10.5$
• D. $11$

Hint:

When the mean of a set includes a variable, substitute the mean formula and solve algebraically for the unknown variable.

Answer 1

The Correct Option is B

Step 1: Recall the formula for mean.
The mean of $n$ numbers is given by: \[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}} \]
Step 2: Apply the given condition.
The mean of the numbers $7, 8, x, 11, 14$ is given as $x$.
Hence, \[ x = \frac{7 + 8 + x + 11 + 14}{5} \]
Step 3: Simplify the equation.
\[ x = \frac{40 + x}{5} \]
Step 4: Multiply both sides by 5.
\[ 5x = 40 + x \]
Step 5: Solve for $x$.
\[ 5x - x = 40 \] \[ 4x = 40 \] \[ x = 10 \]
Step 6: Conclusion.
Therefore, the value of $x$ is $10$.