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Jerry has been a contestant on a game show for the last seven weeks. In the first seven appearances, contestants can win between [tex]$200 and $[/tex]900. On their eighth appearance, they can win [tex]$10,000.

Given Jerry's winnings in the table, describe what would happen to the mean and median if he gets the Week 8 question right.

| Week 1 | Week 2 | Week 3 | Week 4 | Week 5 | Week 6 | Week 7 |
|--------|--------|--------|--------|--------|--------|--------|
| $[/tex]684 | [tex]$770 | $[/tex]481 | [tex]$647 | $[/tex]277 | [tex]$853 | $[/tex]712 |

a. The mean increases by [tex]$1,803, the median increases by $[/tex]698.
b. The mean decreases by [tex]$1,803, the median decreases by $[/tex]698.
c. The mean decreases by [tex]$1,171, the median decreases by $[/tex]14.
d. The mean increases by [tex]$1,171, the median increases by $[/tex]14.

Please select the best answer from the choices provided.


Sagot :

Let's analyze the problem step by step to understand the changes in the mean and median if Jerry wins [tex]$10,000 in Week 8. ### Step 1: Initial Calculations Winnings for the first seven weeks: \[ 684, 770, 481, 647, 277, 853, 712 \] Calculate the initial mean: \[ \text{Mean}_\text{initial} = \frac{684 + 770 + 481 + 647 + 277 + 853 + 712}{7} \] \[ \text{Mean}_\text{initial} = \frac{4424}{7} = 632.0 \] Calculate the initial median: To find the median, we first sort the winnings: \[ 277, 481, 647, 684, 712, 770, 853 \] Since there are 7 numbers, the median is the 4th number in the sorted list: \[ \text{Median}_\text{initial} = 684 \] ### Step 2: Add Week 8 Winnings Adding Jerry's win in Week 8: \[ winnings = [684, 770, 481, 647, 277, 853, 712, 10000] \] ### Step 3: New Calculations Calculate the new mean: \[ \text{Mean}_\text{new} = \frac{684 + 770 + 481 + 647 + 277 + 853 + 712 + 10000}{8} \] \[ \text{Mean}_\text{new} = \frac{14424}{8} = 1803.0 \] Calculate the new median: To find the median of the updated list, we sort it: \[ 277, 481, 647, 684, 712, 770, 853, 10000 \] Since there are now 8 numbers, the median is the average of the 4th and 5th numbers: \[ \text{Median}_\text{new} = \frac{684 + 712}{2} = 698.0 \] ### Step 4: Changes in the Mean and Median Change in mean: \[ \text{Mean Increase} = \text{Mean}_\text{new} - \text{Mean}_\text{initial} \] \[ \text{Mean Increase} = 1803.0 - 632.0 = 1171.0 \] Change in median: \[ \text{Median Increase} = \text{Median}_\text{new} - \text{Median}_\text{initial} \] \[ \text{Median Increase} = 698.0 - 684.0 = 14.0 \] ### Step 5: Conclusion Given the changes calculated: - The mean increases by \$[/tex]1171.0.
- The median increases by \[tex]$14.0. The best answer among the provided options is: \[ d. \text{The mean increases by \$[/tex]1,171, the median increases by \$14.}
\]