if the mean of `6,8,9, x,13,` is `10,` find the value of `x.`

Options

A. 15
B. 14
C. 16
D. 17

Explanation

To find the value of \( x \) in the data set \( 6, 8, 9, x, 13 \) where the mean is given as \( 10 \), we can follow these steps:

### Step 1: Understand the formula for mean
The mean (average) is calculated by taking the sum of all observations and dividing it by the number of observations.

### Step 2: Set up the equation
Given the numbers are \( 6, 8, 9, x, 13 \), we can express the mean as:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
Here, the number of observations is \( 5 \) (since there are 5 numbers).

### Step 3: Substitute the values into the mean formula
We know the mean is \( 10 \), so we can write:
\[ 10 = \frac{6 + 8 + 9 + x + 13}{5} \]

### Step 4: Calculate the sum of the known numbers
First, calculate the sum of the known numbers:
\[ 6 + 8 + 9 + 13 = 36 \]
Now, substitute this back into the equation:
\[ 10 = \frac{36 + x}{5} \]

### Step 5: Cross-multiply to eliminate the fraction
To eliminate the fraction, multiply both sides by \( 5 \):
\[ 10 \times 5 = 36 + x \]
This simplifies to:
\[ 50 = 36 + x \]

### Step 6: Solve for \( x \)
Now, isolate \( x \) by subtracting \( 36 \) from both sides:
\[ x = 50 - 36 \]
\[ x = 14 \]

### Conclusion
The value of \( x \) is \( 14 \).

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