https://file.aiquickdraw.com/mathbot/file/1725023944577x1h5uoea.jpg

Use the table to determine the missing values a–g. For answers that are not whole numbers, round to three decimal places.

Let's analyze the table and fill in the missing values (labeled as $ a $ through $ g $).

### Step 1: Understand the columns
1. **Frequency**: The number of occurrences for each airfare.
2. **Relative Frequency**: The proportion of each airfare's frequency relative to the total frequency.
3. **Cumulative Frequency**: The running total of frequencies up to that point.
4. **Relative Cumulative Frequency**: The running total of relative frequencies up to that point.

### Step 2: Calculate missing values

1. **Total Frequency (a):**
   To find the total frequency $ a $, sum up all the given frequencies:
   \[
   a = 4 + 2 + 1 + 12 + 7 + 2 + 8 + 4 + 2 + 6 + 12 = 60
   \]

2. **Relative Frequency for $999 (b):**
   The relative frequency is given by:
   \[
   b = \frac{\text{Frequency at } \$999}{\text{Total Frequency}} = \frac{1}{60} \approx 0.017
   \]

3. **Cumulative Frequency for $1,035 (c):**
   The cumulative frequency is the sum of frequencies up to and including $1,035:
   \[
   c = 4 + 2 + 1 + 12 = 19
   \]

4. **Relative Cumulative Frequency for $1,133 (d):**
   The relative cumulative frequency up to $1,133:
   \[
   d = \frac{\text{Cumulative Frequency at } \$1,133}{\text{Total Frequency}} = \frac{34}{60} = 0.567
   \]

5. **Cumulative Frequency for $1,205 (e):**
   The cumulative frequency is the sum of frequencies up to and including $1,205:
   \[
   e = 4 + 2 + 1 + 12 + 7 + 2 + 8 = 36
   \]

6. **Relative Cumulative Frequency for $1,245 (f):**
   The relative cumulative frequency up to $1,245:
   \[
   f = \frac{68}{80} = 0.85
   \]

7. **Relative Cumulative Frequency for $1,265 (g):**
   The relative cumulative frequency up to $1,265:
   \[
   g = \frac{80}{80} = 1.000
   \]

### Final Answers:

- $ a = 60 $
- $ b \approx 0.017 $
- $ c = 19 $
- $ d = 0.567 $
- $ e = 36 $
- $ f = 0.85 $
- $ g = 1.000 $

Would you like more details or have any questions? Here are some related questions for further exploration:

1. How does the relative frequency distribution help in understanding the data?
2. What does the cumulative frequency tell us about the data trend?
3. How can this data be used to forecast future airfare prices?
4. What is the significance of rounding relative frequencies to three decimal places?
5. How would the frequency distribution change if a new airfare price was added?

**Tip:** When working with cumulative frequencies, ensure you carefully sum the frequencies to avoid errors in subsequent calculations.

Learn how to analyze frequency distribution and cumulative frequency in airfare data using a detailed example. Understand concepts such as relative frequency and their applications. Suitable for Grades 9-12 students and learners.

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