https://file.aiquickdraw.com/mathbot/file/1726428967874krnpr2tc.jpg

It seems you've uploaded an image of a dataset related to a study by two researchers tracking AIDS patients' survival lengths. I'll help you fill in the missing parts of the table for Researchers A and B.

Let me first summarize the table structure and the steps to fill in the missing details:

### Researcher A:
- **Survival Length (in months)** is already provided in ranges.
- **Frequency**: We need to check how many patients fall within each range.
- **Relative Frequency**: This is calculated as the frequency for a given range divided by the total number of patients (40 in this case).
- **Cumulative Relative Frequency**: This accumulates the relative frequencies as you move down the table.

### Researcher B:
Same structure, and we'll follow similar steps to compute the necessary values for Researcher B.

Let me calculate the missing values now.Here are the calculated values for both Researcher A and Researcher B:

### Researcher A:
- **Frequencies**:  
  \[2, 2, 9, 5, 7, 7, 2, 3\]
- **Relative Frequencies** (calculated by dividing frequency by total patients):  
  \[0.05, 0.05, 0.225, 0.125, 0.175, 0.175, 0.05, 0.075\]
- **Cumulative Relative Frequencies**:  
  \[0.05, 0.10, 0.325, 0.45, 0.625, 0.80, 0.85, 0.925\]

### Researcher B:
- **Frequencies**:  
  \[3, 6, 5, 6, 7, 4, 4, 5\]
- **Relative Frequencies**:  
  \[0.075, 0.15, 0.125, 0.15, 0.175, 0.10, 0.10, 0.125\]
- **Cumulative Relative Frequencies**:  
  \[0.075, 0.225, 0.35, 0.50, 0.675, 0.775, 0.875, 1.0\]

Would you like any additional clarifications or further details?

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Here are some follow-up questions to deepen your understanding:

1. How would you interpret the cumulative relative frequencies in this study?
2. How can you calculate the mean survival time based on the data from both researchers?
3. What might the implications of similar or different survival rates between the two researchers suggest?
4. How would you visualize this data to better understand the distribution?
5. Could this data be used to predict survival times for new patients?

**Tip**: The cumulative relative frequency reaching 1.0 means that 100% of the patients are accounted for across the survival time intervals.

Given two researchers' data sets tracking the survival lengths of AIDS patients in months, complete the frequency, relative frequency, and cumulative relative frequency tables for each researcher.

Learn how to complete frequency distribution tables for two researchers tracking the survival length of AIDS patients in months. This example covers frequency, relative frequency, and cumulative relative frequency calculations using real-world data. Suitable for high school students studying statistics.

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