To determine how the mean and median are affected by the inclusion of the package that weighs 155 ounces, we will first calculate the mean and median of the original six packages, and then evaluate how they change when the 155-ounce package is included.
Original Weights:
- 35, 25, 75, 30, 70, 65 ounces
Step 1: Calculate the Mean of the Original Packages.
Mean = (Sum of weights) / (Number of packages)
Sum = 35 + 25 + 75 + 30 + 70 + 65 = 300 ounces
Mean = 300 / 6 = 50 ounces
Step 2: Calculate the Median of the Original Packages.
To find the median, we first sort the weights:
- Sorted weights: 25, 30, 35, 65, 70, 75
Since there are 6 numbers (an even count), the median will be the average of the two middle numbers (35 and 65): Median = (35 + 65) / 2 = 50 ounces
Step 3: Adding the 155 Ounce Package.
New weights: 25, 30, 35, 65, 70, 75, 155 ounces
Step 4: Calculate the Mean with the 155 Ounce Package.
Sum = 25 + 30 + 35 + 65 + 70 + 75 + 155 = 455 ounces Mean = 455 / 7 = 65.0 ounces
Step 5: Calculate the Median with the 155 Ounce Package.
Sorted weights: 25, 30, 35, 65, 70, 75, 155
Now that there are 7 numbers (an odd count), the median will be the middle number (the 4th number). Median = 65 ounces
Step 6: Determine the Change in Mean and Median.
- Original Mean = 50 ounces → New Mean = 65 ounces ➔ Mean increases by 15 ounces.
- Original Median = 50 ounces → New Median = 65 ounces ➔ Median increases by 15 ounces.
Conclusion: Both the mean and the median increase by 15 ounces when the 155-ounce package is included.
Thus, the answer is:
A. The median and the mean will stay the same.