The mean of eight numbers is 11. The mean of seven of them is 9.5. What is the 8th number?

Group of answer choices

21.5

12.5

8

22

Let's solve the problem step by step.

### Given:
- The mean of eight numbers is 11.
- The mean of seven of these numbers is 9.5.

### To Find:
The 8th number.

### Solution:

1. **Find the sum of all eight numbers:**
   - If the mean of eight numbers is 11, then the sum of these eight numbers is:
     \[
     \text{Sum of 8 numbers} = 11 \times 8 = 88
     \]

2. **Find the sum of the first seven numbers:**
   - If the mean of the first seven numbers is 9.5, then the sum of these seven numbers is:
     \[
     \text{Sum of 7 numbers} = 9.5 \times 7 = 66.5
     \]

3. **Find the 8th number:**
   - The 8th number is the difference between the sum of all eight numbers and the sum of the first seven numbers:
     \[
     \text{8th number} = 88 - 66.5 = 21.5
     \]

### Answer:
The 8th number is **21.5**.

Would you like more details or have any further questions?

### Relative Questions:
1. How do you calculate the mean of a set of numbers?
2. What is the relationship between the mean and the sum of numbers?
3. How would the answer change if the mean of the seven numbers was higher?
4. How do means change if you add or remove numbers from a set?
5. What is the difference between the mean, median, and mode?

### Tip:
Always double-check your calculations when working with averages, especially when given means and totals, as small mistakes can lead to incorrect conclusions.

Learn how to find the 8th number from given means of eight numbers and seven numbers. This problem involves calculating averages and sums, essential in arithmetic and basic algebra. Suitable for students in Grades 6-8.

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