Let's solve the problem step-by-step:
### Original List of Trading Cards
Firstly, consider the original list of trading cards, which is already ordered:
[tex]\[ 382, 421, 524, 553, 564, 591, 615, 626, 683 \][/tex]
### New List of Trading Cards
Suppose that the number 683 in this list is replaced with 422. Thus, the new list of trading cards becomes:
[tex]\[ 382, 421, 524, 553, 564, 591, 615, 626, 422 \][/tex]
Now, we need to sort this updated list to find the median and mean:
[tex]\[ 382, 421, 422, 524, 553, 564, 591, 615, 626 \][/tex]
### Median Calculation
Original List Median:
- The median is the middle number in a sorted list.
- In the original list: [tex]\[ 382, 421, 524, 553, 564, 591, 615, 626, 683 \][/tex]
- The middle number (5th number in this 9-element list): [tex]\( 564 \)[/tex]
Updated List Median:
- In the updated sorted list: [tex]\[ 382, 421, 422, 524, 553, 564, 591, 615, 626 \][/tex]
- The middle number (5th number in this 9-element list): [tex]\( 553 \)[/tex]
Change in Median:
- The median changes from 564 to 553.
- Therefore, the median decreases by [tex]\( 564 - 553 = 11 \)[/tex].
### Mean Calculation
Original List Mean:
- The mean is the sum of the numbers divided by the number of numbers.
- [tex]\[
\text{Mean}_{\text{original}} = \frac{382 + 421 + 524 + 553 + 564 + 591 + 615 + 626 + 683}{9} = 551.0
\][/tex]
Updated List Mean:
- [tex]\[
\text{Mean}_{\text{updated}} = \frac{382 + 421 + 422 + 524 + 553 + 564 + 591 + 615 + 626}{9} = 522.0
\][/tex]
Change in Mean:
- The mean changes from 551.0 to 522.0.
- Therefore, the mean decreases by [tex]\( 551.0 - 522.0 = 29.0 \)[/tex].
### Answer to the Question
\begin{tabular}{|c|c|c|}
\hline
(a) & What happens to the median? & \begin{tabular}{l}
It decreases by 11\\
\end{tabular} \\
\hline
(b) & What happens to the mean? & \begin{tabular}{l}
It decreases by 29 \\
\end{tabular} \\
\hline
\end{tabular}
So, the median decreases by 11 and the mean decreases by 29.
