The mean of 5 observation 3, 5, 6, x and 11 is 7, find the value of x.

Answer

To find the value of \( x \) in the given problem, we need to follow these steps:

### Step 1: Understand the Mean Formula
The mean (average) of a set of observations is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

### Step 2: Set Up the Equation
We know that the mean of the observations \( 3, 5, 6, x, \) and \( 11 \) is \( 7 \). Therefore, we can set up the equation:
\[ 7 = \frac{3 + 5 + 6 + x + 11}{5} \]

### Step 3: Calculate the Sum of Known Observations
First, we calculate the sum of the known observations:
\[ 3 + 5 + 6 + 11 = 25 \]
So we can rewrite our equation as:
\[ 7 = \frac{25 + x}{5} \]

### Step 4: Cross Multiply to Eliminate the Fraction
To eliminate the fraction, we can cross-multiply:
\[ 7 \times 5 = 25 + x \]
This simplifies to:
\[ 35 = 25 + x \]

### Step 5: Solve for \( x \)
Now, we isolate \( x \) by subtracting \( 25 \) from both sides:
\[ x = 35 - 25 \]
Thus, we find:
\[ x = 10 \]

### Final Answer
The value of \( x \) is \( 10 \).

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