Let's analyze the given problem.

You are provided with the number of trading cards owned by 7 students:

371, 400, 448, 501, 532, 543, 628.

Part (a) What happens to the median when 628 changes to 537?

1. First, find the median of the original list:
   Since there are 7 numbers, the median will be the middle value, which is the 4th number. Median (original) = 501.

2. Now, when 628 changes to 537, the new list becomes: 371, 400, 448, 501, 532, 543, 537.

   After sorting, this becomes: 371, 400, 448, 501, 532, 537, 543.

   The median is still the middle number, which is the 4th value: Median (new) = 501.

Answer for (a): The median stays the same.

Part (b) What happens to the mean when 628 changes to 537?

1. First, calculate the original mean: $\text{Mean (original)} = \frac{371 + 400 + 448 + 501 + 532 + 543 + 628}{7} = \frac{3423}{7} = 489$

2. Now, calculate the new mean when 628 changes to 537: $\text{Mean (new)} = \frac{371 + 400 + 448 + 501 + 532 + 543 + 537}{7} = \frac{3332}{7} \approx 476$

Answer for (b): The mean decreases.

Recap:

• (a) The median stays the same.
• (b) The mean decreases.

Would you like further details or explanations on any part of this solution?

Here are 5 related questions for further understanding:

1. How do you calculate the median for an even number of values?
2. What is the effect of an extreme value (outlier) on the mean?
3. How does changing the highest value in a data set affect the range?
4. If the smallest value were changed instead, how would that affect the mean?
5. Can the mean and median ever be the same for a set of numbers?

Tip: The median is resistant to extreme values (outliers), while the mean is more sensitive to such changes.