Let’s solve the problem step by step:

Problem:

We are given a set of numbers: $2, 35, 13, 5, \_, 11, 9, 15, 4$, and the mean of the numbers is 15. We are tasked with finding the missing number ($x$).

Step-by-Step Solution:

1. Mean Formula: $\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}}$ Here, the mean is 15, and there are 9 numbers in total.

2. Total Sum: Using the mean formula: $15 = \frac{\text{Sum of all numbers}}{9}$ Multiply through by 9: $\text{Sum of all numbers} = 15 \times 9 = 135$

3. Sum of Given Numbers: Add the given numbers: $2 + 35 + 13 + 5 + 11 + 9 + 15 + 4 = 94$

4. Find the Missing Number: Let $x$ be the missing number. From the total sum: $94 + x = 135$ Solve for $x$: $x = 135 - 94 = 41$

Final Answer:

The missing number is 41.

Let me know if you'd like further explanation or have questions! Here are some related questions to consider:

1. How do we calculate the mean if multiple numbers are missing?
2. What happens to the mean if one number in the set is removed?
3. Can you identify scenarios where the mean is not a good representation of the dataset?
4. How does the median compare to the mean for this dataset?
5. What is the sum of all given numbers excluding the missing one?

Tip: Double-check your calculations when dealing with multiple steps to avoid small errors.