At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
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: \[ d. \text{The mean increases by \$[/tex]1,171, the median increases by \$14.}
\]
- The median increases by \[tex]$14.0. The best answer among the provided options is: \[ d. \text{The mean increases by \$[/tex]1,171, the median increases by \$14.}
\]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.