Find x, if 9,x,14,18,x,x,8,10 and 4 have a mean of 11.

Answer

To find the value of \( x \) in the given set of numbers \( 9, x, 14, 18, x, x, 8, 10, 4 \) that has a mean of \( 11 \), we can follow these steps:

### Step 1: Understand the formula for mean
The mean is calculated as the sum of all observations divided by the total number of observations.

### Step 2: Write the equation for the mean
Given that the mean is \( 11 \) and there are \( 9 \) observations, we can set up the equation:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \]
This translates to:
\[ 11 = \frac{9 + x + 14 + 18 + x + x + 8 + 10 + 4}{9} \]

### Step 3: Calculate the sum of observations
Now, we can simplify the sum in the numerator:
\[ 9 + 14 + 18 + 8 + 10 + 4 = 63 \]
So, the equation becomes:
\[ 11 = \frac{63 + 3x}{9} \]

### Step 4: Multiply both sides by 9
To eliminate the fraction, multiply both sides by \( 9 \):
\[ 11 \times 9 = 63 + 3x \]
This gives us:
\[ 99 = 63 + 3x \]

### Step 5: Isolate \( 3x \)
Now, subtract \( 63 \) from both sides:
\[ 99 - 63 = 3x \]
This simplifies to:
\[ 36 = 3x \]

### Step 6: Solve for \( x \)
Now, divide both sides by \( 3 \):
\[ x = \frac{36}{3} \]
Thus, we find:
\[ x = 12 \]

### Final Answer
The value of \( x \) is \( 12 \).

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