Question: User: 9,667
11,000
8,668
11,500
10,500
10,500
10,000
10,989
10,989
8,150
9,324
10,000
15,000
10,167
10,000
6,327
9,667
10,000
10,333
10,000
10,000
10,000
9,200
8,658
1. **Stating the problem:** We are given a list of numbers and we want to analyze or summarize them. A common task is to find the mean (average) of these numbers.
2. **Formula for the mean:** The mean $\bar{x}$ of $n$ numbers $x_1, x_2, ..., x_n$ is given by:
$$\bar{x} = \frac{\sum_{i=1}^n x_i}{n}$$
3. **Count the numbers:** There are $23$ numbers in the list.
4. **Sum the numbers:**
$$9,667 + 11,000 + 8,668 + 11,500 + 10,500 + 10,500 + 10,000 + 10,989 + 10,989 + 8,150 + 9,324 + 10,000 + 15,000 + 10,167 + 10,000 + 6,327 + 9,667 + 10,000 + 10,333 + 10,000 + 10,000 + 9,200 + 8,658$$
Calculate the sum step-by-step:
- $9,667 + 11,000 = 20,667$
- $20,667 + 8,668 = 29,335$
- $29,335 + 11,500 = 40,835$
- $40,835 + 10,500 = 51,335$
- $51,335 + 10,500 = 61,835$
- $61,835 + 10,000 = 71,835$
- $71,835 + 10,989 = 82,824$
- $82,824 + 10,989 = 93,813$
- $93,813 + 8,150 = 101,963$
- $101,963 + 9,324 = 111,287$
- $111,287 + 10,000 = 121,287$
- $121,287 + 15,000 = 136,287$
- $136,287 + 10,167 = 146,454$
- $146,454 + 10,000 = 156,454$
- $156,454 + 6,327 = 162,781$
- $162,781 + 9,667 = 172,448$
- $172,448 + 10,000 = 182,448$
- $182,448 + 10,333 = 192,781$
- $192,781 + 10,000 = 202,781$
- $202,781 + 10,000 = 212,781$
- $212,781 + 9,200 = 221,981$
- $221,981 + 8,658 = 230,639$
5. **Calculate the mean:**
$$\bar{x} = \frac{230,639}{23}$$
6. **Simplify the fraction:**
$$\bar{x} = \frac{\cancel{230,639}}{\cancel{23}} = 10,028.65$$
7. **Interpretation:** The average of the given numbers is approximately $10,028.65$.
**Final answer:**
$$\boxed{10,028.65}$$