The arithmetic mean of 6, 10, x and 12 is 8 . The value of x is

Options

A. 3
B. 4
C. 5
D. 6

Answer

To find the value of \( x \) given that the arithmetic mean of the numbers 6, 10, \( x \), and 12 is 8, we can follow these steps:

### Step 1: Write the formula for the arithmetic mean.
The arithmetic mean (average) is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Total number of observations}} \]

### Step 2: Substitute the known values into the formula.
We know the mean is 8, and we have four observations: 6, 10, \( x \), and 12. Therefore, we can set up the equation:
\[ 8 = \frac{6 + 10 + x + 12}{4} \]

### Step 3: Multiply both sides by the total number of observations.
To eliminate the fraction, multiply both sides of the equation by 4:
\[ 8 \times 4 = 6 + 10 + x + 12 \]
This simplifies to:
\[ 32 = 6 + 10 + x + 12 \]

### Step 4: Simplify the right side of the equation.
Now, add the constant numbers on the right side:
\[ 32 = 28 + x \]

### Step 5: Solve for \( x \).
To isolate \( x \), subtract 28 from both sides:
\[ 32 - 28 = x \]
This gives us:
\[ x = 4 \]

### Conclusion:
The value of \( x \) is 4.

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