Aziz wonders how many pieces of pizza people tend to eat at a pizza party. He surveys 10 people at the end of a pizza party and asks them how many pieces of pizza they ate. A list of his results follows. Aziz uses his results to calculate that the mean number of pieces of pizza eaten is 3.5. Number of Pieces of Pizza Eaten: 1, 2, 2, 2, 3, 4, 4, 5, 6, 6 After calculating the mean, Aziz realizes he forgot to include himself! He ate 6 pieces of pizza. Describe how adding another “6” to the dataset will impact the mean.(1 point) Responses The mean will stay the same. The mean will stay the same. The mean will increase by a lot. The mean will no longer be in the center of the data. The mean will increase by a lot. The mean will no longer be in the center of the data. The mean will increase slightly but will still be in the center of the data. The mean will increase slightly but will still be in the center of the data. The mean will decrease slightly but will still be in the center of the data.

Question

GPT-4o mini · Answer

To analyze how adding Aziz's 6 pieces of pizza to the dataset impacts the mean, let's first calculate the new mean after including his contribution.

Original dataset of pieces of pizza eaten (10 people): 1, 2, 2, 2, 3, 4, 4, 5, 6, 6
- Sum of original data = 1 + 2 + 2 + 2 + 3 + 4 + 4 + 5 + 6 + 6 = 35
- Mean of original data = 35 / 10 = 3.5
Adding Aziz's contribution (6 pieces) increases the dataset to 11 people:
- New dataset: 1, 2, 2, 2, 3, 4, 4, 5, 6, 6, 6
- New sum = 35 + 6 = 41
- New mean = 41 / 11 ≈ 3.727

The mean has increased from 3.5 to approximately 3.727, which is a slight increase.

Additionally, since the new mean (approximately 3.727) is still close to the center of the data (the values range from 1 to 6), it retains its position relative to the dataset.

Therefore, the correct response is: "The mean will increase slightly but will still be in the center of the data."