https://file.aiquickdraw.com/mathbot/file/1727026645783c6z83prc.jpg

Let's analyze the problem presented in the image.

We are given the monthly rent payments for 10 people, already sorted in ascending order:  
**7300, 8850, 9750, 10,300, 10,350, 10,500, 10,800, 11,100, 11,250, 13,300**

The problem asks what happens to the mean (media) and the median (mediana) when one person's rent changes from **$13,300** to **$9300**.

### (a) Effect on the Mean (Media)
The **mean** is the sum of all the rent values divided by the number of people (10 in this case).

Let's calculate the current mean before the change, and then again after the rent of $13,300 changes to $9300.

#### (b) Effect on the Median (Mediana)
The **median** is the middle value in a sorted list. For an even number of data points (10), the median is the average of the 5th and 6th values.

I'll now calculate both the mean and median, before and after the change, to determine their behavior.Here are the results:

1. **Mean (Media)**:
   - **Before the change**: $10,350
   - **After the change**: $9,950
   - The mean **decreases** when the rent changes from $13,300 to $9,300.

2. **Median (Mediana)**:
   - **Before the change**: $10,425
   - **After the change**: $10,425
   - The median **remains the same** because the middle values are not affected by this change in the highest rent.

### Summary:
- **(a)** The mean decreases.
- **(b)** The median stays the same.

Would you like more details or clarifications? Here are five related questions you could explore:

1. How do outliers affect the mean versus the median?
2. What would happen if another high rent were reduced instead?
3. How does the range of rents change with this adjustment?
4. What would happen if multiple rents changed, not just one?
5. How is the mode (if there is one) affected by this change?

**Tip:** When comparing mean and median, remember that the mean is more sensitive to extreme values (outliers), while the median reflects the central tendency better in such cases.

Given the monthly rents (in dollars) paid by 10 people: 7300, 8850, 9750, 10,300, 10,350, 10,500, 10,800, 11,100, 11,250, 13,300. What happens to the mean and median if the highest rent ($13,300) is reduced to $9,300?

Explore the effect of reducing the highest rent from $13,300 to $9,300 on the mean and median of a data set. This problem provides a detailed analysis of how changes in data points influence statistical measures like mean and median. Suitable for students in Grades 8-10.

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