https://file.aiquickdraw.com/mathbot/file/1726696274251c3p5opp3.jpg

Let's analyze the problem from the image. The set of numbers represents collectible card values for 10 students. The values are already ordered from least to greatest:

**387, 430, 457, 471, 476, 538, 557, 594, 595, 685**

The question asks what happens to the **median** and **mean** when the number **685** is changed to **585**.

### a) What happens to the median?
- The median is the middle value in a sorted dataset. Since there are 10 numbers, the median is the average of the 5th and 6th values in the ordered list:
  \[
  \text{Median} = \frac{476 + 538}{2} = 507
  \]
Changing **685** to **585** does not affect the middle values (476 and 538). Therefore, the median **remains the same**.

### b) What happens to the mean?
- The mean is calculated by summing all the numbers and dividing by the number of values. Let's compute the original mean and the new mean after replacing **685** with **585**.

#### Original mean:
\[
\text{Original sum} = 387 + 430 + 457 + 471 + 476 + 538 + 557 + 594 + 595 + 685 = 5190
\]
\[
\text{Original mean} = \frac{5190}{10} = 519
\]

#### New mean (after changing 685 to 585):
\[
\text{New sum} = 5190 - 685 + 585 = 5090
\]
\[
\text{New mean} = \frac{5090}{10} = 509
\]

So, the mean **decreases** from **519** to **509**.

### Final answers:
a) The **median remains the same**.  
b) The **mean decreases**.

Would you like further details or have any other questions?

Here are 5 related questions:
1. How is the median affected if the change were in one of the middle values?
2. How does the standard deviation change with this modification?
3. What happens to the range of the dataset with this change?
4. How would removing a value instead of changing it affect the median and mean?
5. How does the mode change when you modify values in a dataset?

**Tip:** The median is less sensitive to extreme values compared to the mean, making it a better measure of central tendency in skewed distributions.

Suppose that the number 685 in the list changes to 585. What happens to the median and mean?

Analyze how changing the value 685 to 585 affects the mean and median in a set of 10 collectible card numbers. This problem explores key concepts in statistics, including how to calculate the mean and median, and the impact of altering values in a dataset.

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