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. Following is a list of his results. Find and interpret the mean of his data.

Question

Number of Pieces of Pizza Eaten: 1, 2, 2, 2, 3, 4, 4, 5, 6, 6(1 point)
Responses

The mean number of pieces of pizza eaten is 3.5. This means each person at the pizza party ate at least 3.5 pieces of pizza.
The mean number of pieces of pizza eaten is 3.5. This means each person at the pizza party ate at least 3.5 pieces of pizza.

The mean number of pieces of pizza eaten is 3.5. This means people ate around 3.5 pieces of pizza on average at the pizza party.
The mean number of pieces of pizza eaten is 3.5. This means people ate around 3.5 pieces of pizza on average at the pizza party.

The mean number of pieces of pizza eaten is 5. This means the difference between the greatest number of pieces of pizza eaten and the least number of pieces of pizza eaten is 5.
The mean number of pieces of pizza eaten is 5. This means the difference between the greatest number of pieces of pizza eaten and the least number of pieces of pizza eaten is 5.

The mean number of pieces of pizza eaten is 35. This means people ate a total of 35 pieces of pizza at the pizza party.
Use the table to answer the question.

Number of Siblings	Number of 6th Graders
0	3
1	12
2	5
3	2
4	0
5	1
Kaylen wants to know how many siblings 6th graders have. She surveys the 6th graders on her soccer team. Her results are given in the table. What is the mean number of siblings for the 6th graders that she surveyed? Round your answer to the nearest hundredth.

(1 point)
Responses

1.43 siblings
1.43 siblings

2.50 siblings
2.50 siblings

3.83 siblings
3.83 siblings

1.67 siblings
Aziz wonders how many pieces of pizza people tend to eat at a pizza party. He surveys 11 people at the end of a pizza party and asks them how many pieces of pizza they ate. His results follow. Find and interpret the median of his data.

Number of Pieces of Pizza Eaten: 6, 2, 1, 2, 4, 5, 2, 2, 4, 6, 7(1 point)
Responses

The median number of pieces of pizza eaten is 3.73. This means on average, each person ate 3.73 pieces of pizza at the party.
The median number of pieces of pizza eaten is 3.73. This means on average, each person ate 3.73 pieces of pizza at the party.

The median number of pieces of pizza eaten is 5. This means about half the people at the party ate 5 or more pieces of pizza, and about half the people at the party ate 5 or fewer pieces of pizza.
The median number of pieces of pizza eaten is 5. This means about half the people at the party ate 5 or more pieces of pizza, and about half the people at the party ate 5 or fewer pieces of pizza.

The median number of pieces of pizza eaten is 3. This means about half the people at the party ate 3 or more pieces of pizza, and about half the people at the party ate 3 or fewer pieces of pizza.
The median number of pieces of pizza eaten is 3. This means about half the people at the party ate 3 or more pieces of pizza, and about half the people at the party ate 3 or fewer pieces of pizza.

The median number of pieces of pizza eaten is 4. This means about half the people at the party ate 4 or more pieces of pizza, and about half the people at the party ate 4 or fewer pieces of pizza.
Use the table to answer the question.

Number of Siblings	Number of 6th Graders
0	3
1	12
2	5
3	2
4	0
5	2
Kaylen wants to know how many siblings 6th graders have. She surveys the 6th graders on her soccer team. Her results are given in the table. What is the median number of siblings for the 6th graders that she surveyed?

(1 point)
Responses

1 sibling
1 sibling

3 siblings
3 siblings

2.5 siblings
2.5 siblings

1.58 siblings
Yasmine works as a server in a restaurant and earns different amounts in tips each night. Her median earnings in tips over the course of 8 nights of work is $39.50. Her minimum tip earnings were $10.45, and her maximum tip earnings were $96.78. What is a possible dataset of tip earnings?(1 point)
Responses

{$10.45,$20.50,$35.80,$38.10,$40.90,$45.90,$105.96,$96.78}
left brace $10.45 comma $20.50 comma $35.80 comma $38.10 comma $40.90 comma $45.90 comma $105.96 comma $96.78 right brace

{$10.45,$20.50,$35.80,$38.10,$39.50,$42.50,$45.90,$79.60,$96.78}
left brace $10.45 comma $20.50 comma $35.80 comma $38.10 comma $39.50 comma $42.50 comma $45.90 comma $79.60 comma $96.78 right brace

{$10.45,$39.50,$39.50,$78.10,$80.90,$95.90,$109.40,$110.80}
left brace $10.45 comma $39.50 comma $39.50 comma $78.10 comma $80.90 comma $95.90 comma $109.40 comma $110.80 right brace

{$10.45,$20.50,$35.80,$38.10,$40.90,$45.90,$79.60,$96.78}

GPT-4o mini · Answer

Let's address each of the questions step by step, providing calculations and interpretations for each case.

Finding the Mean Pizza Consumption

Data: 1, 2, 2, 2, 3, 4, 4, 5, 6, 6

Calculate the mean:
- Sum of all pieces of pizza: $1 + 2 + 2 + 2 + 3 + 4 + 4 + 5 + 6 + 6 = 35$
- Number of people: $10$
- Mean = Total Pizza / Number of People = $35 / 10 = 3.5$
Interpretation:
- The correct interpretation is: "The mean number of pieces of pizza eaten is 3.5. This means people ate around 3.5 pieces of pizza on average at the pizza party."

Finding the Mean Number of Siblings

Data from the Table:

0 siblings: 3 students
1 sibling: 12 students
2 siblings: 5 students
3 siblings: 2 students
4 siblings: 0 students
5 siblings: 1 student

Calculate the mean number of siblings:
- Total number of siblings: \[ (0 \times 3) + (1 \times 12) + (2 \times 5) + (3 \times 2) + (4 \times 0) + (5 \times 1) = 0 + 12 + 10 + 6 + 0 + 5 = 33 \]
- Total number of students = 3 + 12 + 5 + 2 + 0 + 1 = 23
- Mean = Total Siblings / Total Students = $33 / 23 \approx 1.43$
Interpretation:
- The correct answer is: "1.43 siblings"

Finding the Median Pizza Consumption

Data: 6, 2, 1, 2, 4, 5, 2, 2, 4, 6, 7

Sort the data: 1, 2, 2, 2, 2, 4, 4, 5, 6, 6, 7
Calculate the median:
- Since there are 11 numbers (an odd count), the median is the middle number, which is the 6th number in the sorted list: 4.
Interpretation:
- The correct interpretation is: "The median number of pieces of pizza eaten is 4. This means about half the people at the party ate 4 or more pieces of pizza, and about half the people at the party ate 4 or fewer pieces of pizza."

Finding the Median Number of Siblings

Data from the Table:

0 siblings: 3 students
1 sibling: 12 students
2 siblings: 5 students
3 siblings: 2 students
4 siblings: 0 students
5 siblings: 1 student

Construct the dataset:
- 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 5
Count of students: 23.
Median:
- Since there are 23 numbers (an odd count), the median is the middle number, which is the 12th number in the sorted list: 1.
Interpretation:
- The correct answer is: "1 sibling"

Finding Possible Dataset of Tips

The median earnings in tips over the course of 8 nights of work is $39.50, which means the average of the 4th and 5th values in the sorted order of 8 tips is $39.50.
Since the minimum tip is $10.45 and the maximum is $96.78, the possible dataset must include values that meet these criteria.

Check the datasets:

Option 1: Invalid, as it has values exceeding the maximum.
Option 2: Contains $39.50 and fits within the limits, so this is a valid dataset.
Option 3: Invalid, as it has values exceeding the maximum.
Option 4: Invalid, as it has values exceeding the maximum.

Conclusion: The valid dataset is:

{$10.45, $20.50, $35.80, $38.10, $39.50, $42.50, $45.90, $79.60, $96.78}.

Final Answers Summary:

Mean pizza consumption: 3.5
Mean siblings: 1.43
Median pizza consumption: 4
Median siblings: 1
Possible dataset of tips: {$10.45, $20.50, $35.80, $38.10, $39.50, $42.50, $45.90, $79.60, $96.78}.