If the arithmetic mean of 7, 5, 13, x, 9 and 10 is 10, then value of x is

Answer

To find the value of \( x \) given that the arithmetic mean of the numbers 7, 5, 13, \( x \), 9, and 10 is 10, we can follow these steps:

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

### Step 2: Identify the numbers and the mean.
In this case, the numbers are 7, 5, 13, \( x \), 9, and 10. The mean is given as 10.

### Step 3: Set up the equation.
The total number of observations is 6 (since we have six numbers). Therefore, we can set up the equation:
\[ 10 = \frac{7 + 5 + 13 + x + 9 + 10}{6} \]

### Step 4: Calculate the sum of the known numbers.
Now, calculate the sum of the known numbers:
\[ 7 + 5 + 13 + 9 + 10 = 44 \]

### Step 5: Substitute the sum into the equation.
Substituting the sum back into the equation gives:
\[ 10 = \frac{44 + x}{6} \]

### Step 6: Multiply both sides by 6 to eliminate the fraction.
To eliminate the fraction, multiply both sides by 6:
\[ 60 = 44 + x \]

### Step 7: Solve for \( x \).
Now, isolate \( x \) by subtracting 44 from both sides:
\[ x = 60 - 44 \]
\[ x = 16 \]

### Conclusion:
The value of \( x \) is 16.

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