To solve this problem, we need to calculate the mean and median of the shirt prices before and after adding the new shirt price and then compare the changes.
First, let's calculate the mean of the original shirt prices:
Original shirt prices: [tex]$30, $[/tex]24, [tex]$29, $[/tex]40, [tex]$19, $[/tex]35
Step 1: Calculate the sum of the original shirt prices.
Sum = [tex]$30 + $[/tex]24 + [tex]$29 + $[/tex]40 + [tex]$19 + $[/tex]35 = [tex]$177
Step 2: Calculate the number of shirts.
Number of shirts initially = 6
Step 3: Find the mean (average) shirt price by dividing the sum by the number of shirts.
Mean = Sum / Number of shirts = $[/tex]177 / 6 ≈ [tex]$29.50
Now, let's calculate the median of the original shirt prices:
For the median, we need to sort the prices and find the middle value(s).
Sorted shirt prices: $[/tex]19, [tex]$24, $[/tex]29, [tex]$30, $[/tex]35, [tex]$40
There are six shirts, which is an even number, so the median will be the average of the middle two values.
Middle values: $[/tex]29 and [tex]$30
Median = ($[/tex]29 + [tex]$30) / 2 = $[/tex]59 / 2 = [tex]$29.50
So, both the original mean and median of shirt prices are $[/tex]29.50.
Next, we'll include the additional shirt price of [tex]$50 and perform the same calculations.
Updated shirt prices: $[/tex]30, [tex]$24, $[/tex]29, [tex]$40, $[/tex]19, [tex]$35, $[/tex]50
Step 1: Calculate the sum of the updated shirt prices.
Sum = [tex]$177 + $[/tex]50 = [tex]$227
Step 2: Calculate the number of shirts after adding the new shirt.
Number of shirts now = 7
Step 3: Find the new mean shirt price.
Mean = Sum / Number of shirts = $[/tex]227 / 7 ≈ [tex]$32.43
Now let's calculate the median of the updated shirt prices:
Sorted updated shirt prices: $[/tex]19, [tex]$24, $[/tex]29, [tex]$30, $[/tex]35, [tex]$40, $[/tex]50
Since there are now seven shirts (an odd number), the median will be the middle value.
Median = [tex]$30 (the fourth value in the sorted list)
Now we can observe the changes:
Original mean: $[/tex]29.50
New mean: [tex]$32.43
Change in mean: $[/tex]32.43 - [tex]$29.50 = $[/tex]2.93
Original median: [tex]$29.50
New median: $[/tex]30
Change in median: [tex]$30 - $[/tex]29.50 = [tex]$0.50
The mean has increased by $[/tex]2.93, while the median has increased by $0.50.
The mean is influenced more by the addition of the new shirt price, because the change in the mean is greater than the change in the median.
Therefore, the correct answer is: The mean increases more.
