A magazine published data on the best small firms in a certain year. These were firms which had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the chief executive officers for the first 64 ranked firms. Frequency Relative Frequency Age 40-44 3 45-49 11 50-54 19 55-59 18 60-64 10 65-69 2 70-74 1 Cumulative Relative Frequency (a) What is the frequency for CEO ages between (but not including) 54 and 65? (Enter your answer as a whole number.) 26, (b) What percentage of CEOs are 65 years or older? (Round your answer to the nearest whole number) 6 X% (c) What is the relative frequency of ages under 507 (Round your answer to two decimal places.) 0.23 (d) What is the cumulative relative frequency for CEOs younger than 55? (Round your answer to two decimal places.) 0.47 (e) Which graph shows the relative frequency? Relative Frequency 1.0 0.8 0.6 Relative Frequency 10 08 06

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### Analyzing CEO Age Demographics in Top Small Firms

A magazine published data on the best small firms in a certain year. These were firms that had been publicly traded for at least a year, had a stock price of at least $5 per share, and had reported annual revenue between $5 million and $1 billion. The table below displays the ages of the chief executive officers (CEOs) for the first 64 ranked firms.

| Age   | Frequency | Relative Frequency | Cumulative Relative Frequency |
|-------|-----------|--------------------|------------------------------|
| 40-44 | 4         |                    |                              |
| 45-49 | 8         |                    |                              |
| 50-54 | 19        |                    |                              |
| 55-59 | 19        |                    |                              |
| 60-64 | 18        |                    |                              |
| 65-69 | 5         |                    |                              |
| Total | 73        |                    |                              |

#### Questions:
1. **What is the frequency for CEO ages between (but not including) 54 and 55?**
   - Answer: 20

2. **What percentage of CEOs are 65 years or older?**
   - Answer: 7%

3. **What is the relative frequency of ages under 50?**
   - Answer: 0.22

4. **What is the cumulative relative frequency for CEOs younger than 55?**
   - Answer: 0.47

5. **Which graph shows the relative frequency?**
   - The answer to this question is determined by comparing the provided graph images and identifying the correct graph that accurately represents the relative frequencies as per the table data.

#### Explanation of Graphs:
- **Relative Frequency Graph:** This bar graph helps to compare the proportional representation of different age groups among CEOs. Each bar height represents the relative frequency calculated by dividing the frequency of each age group by the total number of CEOs surveyed.
  
- **Cumulative Relative Frequency Graph:** This graph would show the running total of the relative frequencies up to the certain age, helping to identify how the proportion accumulates across the age ranges listed.

By using these tools and analysis, educational users can better understand the age distribution among CEOs in prominent small firms and how to interpret such demographic data for various evaluations and decisions.
Transcribed Image Text:### Analyzing CEO Age Demographics in Top Small Firms A magazine published data on the best small firms in a certain year. These were firms that had been publicly traded for at least a year, had a stock price of at least $5 per share, and had reported annual revenue between $5 million and $1 billion. The table below displays the ages of the chief executive officers (CEOs) for the first 64 ranked firms. | Age | Frequency | Relative Frequency | Cumulative Relative Frequency | |-------|-----------|--------------------|------------------------------| | 40-44 | 4 | | | | 45-49 | 8 | | | | 50-54 | 19 | | | | 55-59 | 19 | | | | 60-64 | 18 | | | | 65-69 | 5 | | | | Total | 73 | | | #### Questions: 1. **What is the frequency for CEO ages between (but not including) 54 and 55?** - Answer: 20 2. **What percentage of CEOs are 65 years or older?** - Answer: 7% 3. **What is the relative frequency of ages under 50?** - Answer: 0.22 4. **What is the cumulative relative frequency for CEOs younger than 55?** - Answer: 0.47 5. **Which graph shows the relative frequency?** - The answer to this question is determined by comparing the provided graph images and identifying the correct graph that accurately represents the relative frequencies as per the table data. #### Explanation of Graphs: - **Relative Frequency Graph:** This bar graph helps to compare the proportional representation of different age groups among CEOs. Each bar height represents the relative frequency calculated by dividing the frequency of each age group by the total number of CEOs surveyed. - **Cumulative Relative Frequency Graph:** This graph would show the running total of the relative frequencies up to the certain age, helping to identify how the proportion accumulates across the age ranges listed. By using these tools and analysis, educational users can better understand the age distribution among CEOs in prominent small firms and how to interpret such demographic data for various evaluations and decisions.
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