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Let's solve the problem step by step.

### Initial Information:
The monthly rents for 10 people (already ordered) are:
\[
885, 895, 990, 1035, 1050, 1060, 1075, 1080, 1100, 1800
\]

Now, one person moves, and their rent decreases from **$1800** to **$1150**. We need to calculate the changes to:
1. The **mean** rent.
2. The **median** rent.

---

### Part (a): Effect on the Mean

The **mean** is calculated as the sum of all the rents divided by the number of people. Initially, the sum of the rents is:
\[
885 + 895 + 990 + 1035 + 1050 + 1060 + 1075 + 1080 + 1100 + 1800 = 11970
\]

The initial mean is:
\[
\frac{11970}{10} = 1197
\]

Now, if the rent changes from $1800$ to $1150$, the new sum of the rents becomes:
\[
11970 - 1800 + 1150 = 11320
\]

The new mean is:
\[
\frac{11320}{10} = 1132
\]

So, the mean **decreases** by:
\[
1197 - 1132 = 65
\]

---

### Part (b): Effect on the Median

The **median** is the middle value when the data is ordered. Since there are 10 people, the median is the average of the 5th and 6th values.

Initially, the middle values are:
\[
\frac{1050 + 1060}{2} = 1055
\]

When the rent of $1800$ changes to $1150$, the new ordered list of rents is:
\[
885, 895, 990, 1035, 1050, 1060, 1075, 1080, 1100, 1150
\]

The middle values remain the same ($1050$ and $1060$), so the median remains:
\[
\frac{1050 + 1060}{2} = 1055
\]

Thus, the **median stays the same**.

---

### Final Answers:
- **Mean:** It decreases by **$65**.
- **Median:** It stays the same.

Would you like more details or have any other questions?

Here are 5 related questions to expand this topic:
1. How does the range of the data change after the rent decreases?
2. How would the median change if two people's rents were adjusted?
3. What is the effect on the mode if $1800$ was the most frequent rent?
4. How does standard deviation change with this rent reduction?
5. How would removing the highest rent from the dataset affect the mean?

**Tip**: When calculating the mean, always ensure to sum the values correctly before dividing by the total number of data points.

The monthly rents (in dollars) paid by 10 people are given below: 885, 895, 990, 1035, 1050, 1060, 1075, 1080, 1100, 1800. Suppose that one of the people moves. His rent changes from $1800 to $1150. What happens to the mean and the median?

Explore how changing the monthly rent affects the mean and median in a statistics problem. Given a dataset of rents, see how the mean decreases by $65 when the highest rent changes from $1800 to $1150, while the median remains the same at $1055. Suitable for students in Grades 9-12.

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