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The question in the image provides two series of numbers and asks for the comparison of their averages and standard deviations.

### Series A:
6, 7, 8, 9

### Series B:
3, 5, 7, 9, 11

#### Step 1: Calculate the average (mean) of both series

1. **For Series A:**
   \[
   \text{Average of A} = \frac{6 + 7 + 8 + 9}{4} = \frac{30}{4} = 7.5
   \]

2. **For Series B:**
   \[
   \text{Average of B} = \frac{3 + 5 + 7 + 9 + 11}{5} = \frac{35}{5} = 7
   \]

#### Step 2: Calculate the standard deviation of both series

1. **Standard deviation for Series A:**
   - Mean is 7.5
   \[
   \text{Variance of A} = \frac{(6-7.5)^2 + (7-7.5)^2 + (8-7.5)^2 + (9-7.5)^2}{4}
   = \frac{(1.5)^2 + (0.5)^2 + (0.5)^2 + (1.5)^2}{4}
   = \frac{2.25 + 0.25 + 0.25 + 2.25}{4} = \frac{5}{4} = 1.25
   \]
   \[
   \text{Standard deviation of A} = \sqrt{1.25} \approx 1.118
   \]

2. **Standard deviation for Series B:**
   - Mean is 7
   \[
   \text{Variance of B} = \frac{(3-7)^2 + (5-7)^2 + (7-7)^2 + (9-7)^2 + (11-7)^2}{5}
   = \frac{16 + 4 + 0 + 4 + 16}{5} = \frac{40}{5} = 8
   \]
   \[
   \text{Standard deviation of B} = \sqrt{8} \approx 2.828
   \]

### Conclusion:
- **Averages:** The averages of the two series are **different** (7.5 for Series A and 7 for Series B).
- **Standard deviations:** The standard deviations are also **different** (approximately 1.118 for Series A and 2.828 for Series B).

Thus, the correct answers would be:
- The averages are different.
- The standard deviations are different.

Would you like to explore these calculations in more depth?

### Related Questions:
1. What happens to the standard deviation if we increase all numbers in a series by a constant?
2. How do you calculate the variance of a data set in general?
3. What is the relationship between variance and standard deviation?
4. Why is the standard deviation of Series B larger than that of Series A?
5. How would the calculations change if Series A and Series B had the same number of elements?

**Tip:** The standard deviation is sensitive to the spread of the numbers—wider ranges result in larger deviations!

The image presents two series of numbers and asks for a comparison of their averages and standard deviations.

Series A: 6, 7, 8, 9
Series B: 3, 5, 7, 9, 11

Explore the calculation of averages and standard deviations for two series of numbers: Series A (6, 7, 8, 9) and Series B (3, 5, 7, 9, 11). Learn how to compute the mean and variance, and compare the statistical differences between the two series. Suitable for students in Grades 9-12.

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