Question

topic 3 drawing inferences

1. create a dot plot to show the number of volunteer hours worked for each student over ten weeks. be sure to provide a title and a key.
2. describe the distribution of each data set.
3. determine the mean number of volunteer hours worked per week for each student.
4. predict the number of volunteer hours worked for each student at 24 weeks.

Explanation:

Step1: Extract Miguel's data points

From dot plot: 3,4,5,6,7,8,8,9,9,9

Step2: Calculate Miguel's mean

Sum: $3+4+5+6+7+8+8+9+9+9=68$; Mean: $\frac{68}{10}=6.8$

Step3: Extract Alejandra's data points

From dot plot: 3,4,5,5,6,6,7,8,9,9

Step4: Calculate Alejandra's mean

Sum: $3+4+5+5+6+6+7+8+9+9=62$; Mean: $\frac{62}{10}=6.2$

Step5: Predict Miguel's 24-week hours

Multiply mean by 24: $6.8 \times 24=163.2$

Step6: Predict Alejandra's 24-week hours

Multiply mean by 24: $6.2 \times 24=148.8$

Answer:

1. Dot Plot Titles & Key:

• Miguel's Plot: Miguel's Weekly Volunteer Hours (10 Weeks); Key: Each dot = 1 week
• Alejandra's Plot: Alejandra's Weekly Volunteer Hours (10 Weeks); Key: Each dot = 1 week

1. Distribution Descriptions:

• Miguel's data: Skewed left, with the highest frequency (most dots) at 9 hours, and fewer values at lower hour counts.
• Alejandra's data: Roughly symmetric, with frequencies evenly spread across 3-9 hours, no strong skew.

1. Mean Hours per Week:

• Miguel: 6.8 hours
• Alejandra: 6.2 hours

1. 24-Week Predictions:

• Miguel: 163.2 hours
• Alejandra: 148.8 hours