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We are given the set of numbers: \( 11, 8, 14, 14, x \), and the mean of these numbers is 13. We are tasked with finding the value of \( x \).

The mean of a set of numbers is calculated as:

\[
\text{Mean} = \frac{\text{Sum of the numbers}}{\text{Total number of values}}
\]

In this case, the mean is 13, and there are 5 numbers. Therefore, we can write the equation as:

\[
13 = \frac{11 + 8 + 14 + 14 + x}{5}
\]

Now, solve for \( x \):

1. First, find the sum of the known numbers:

\[
11 + 8 + 14 + 14 = 47
\]

2. Substitute this sum into the equation:

\[
13 = \frac{47 + x}{5}
\]

3. Multiply both sides of the equation by 5 to eliminate the denominator:

\[
13 \times 5 = 47 + x
\]

\[
65 = 47 + x
\]

4. Finally, solve for \( x \) by subtracting 47 from both sides:

\[
x = 65 - 47
\]

\[
x = 18
\]

So, the value of \( x \) is **18**.

Do you need further clarification or details? Here are some related questions to explore:

1. How would the mean change if the value of \( x \) were different?
2. What would be the median of the set \( 11, 8, 14, 14, 18 \)?
3. How do you find the mode of a set of numbers?
4. Can you calculate the range of the set once \( x \) is known?
5. How is the mean affected if one of the numbers is doubled?

**Tip:** To find the mean of a set, always remember to divide the total sum by the number of values in the set.

Given the set of numbers 11, 8, 14, 14, x. The mean of the numbers is 13. Find the value of x.

Solve the problem of finding the unknown value x in the set 11, 8, 14, 14, x, given the mean is 13. The solution involves basic arithmetic and algebra concepts. Suitable for Grades 6-8 students.

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