If the mean of 20, 18 ,13 ,12, x and 10 is 15, then find the value of x.

Answer

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

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

### Step 2: Identify the given values
From the problem, we know:
- The numbers are: 20, 18, 13, 12, \( x \), and 10.
- The mean is given as 15.
- The number of observations is 6 (since there are 6 numbers).

### Step 3: Set up the equation using the mean formula
Using the mean formula, we can set up the equation:
\[ 15 = \frac{20 + 18 + 13 + 12 + x + 10}{6} \]

### Step 4: Calculate the sum of the known numbers
First, we will calculate the sum of the known numbers:
\[ 20 + 18 + 13 + 12 + 10 = 73 \]
So, we can rewrite the equation as:
\[ 15 = \frac{73 + x}{6} \]

### Step 5: Multiply both sides by 6 to eliminate the fraction
To eliminate the fraction, multiply both sides by 6:
\[ 15 \times 6 = 73 + x \]
This simplifies to:
\[ 90 = 73 + x \]

### Step 6: Solve for \( x \)
Now, we can isolate \( x \) by subtracting 73 from both sides:
\[ x = 90 - 73 \]
Calculating this gives:
\[ x = 17 \]

### Conclusion
Therefore, the value of \( x \) is \( 17 \).

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