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The problem involves comparing the number of words learned by two groups (Group A and Group B) after a study session.

Here’s the data from the image:

| Number of Words Learned | Group A | Group B |
|-------------------------|---------|---------|
| **1**                   | 8       | 6       |
| **2**                   | 7       | 9       |
| **3**                   | 12      | 11      |
| **4**                   | 9       | 9       |
| **5**                   | 11      | 12      |
| **6**                   | 13      | 11      |
| **7**                   | 12      | 12      |

### Steps to Solve:
1. **Calculate the Mean (Average) for Each Group:**
   - For Group A: \( \text{Mean}_A = \frac{8 + 7 + 12 + 9 + 11 + 13 + 12}{7} \)
   - For Group B: \( \text{Mean}_B = \frac{6 + 9 + 11 + 9 + 12 + 11 + 12}{7} \)

2. **Calculate the Variance for Each Group:**
   - Variance measures how far the numbers in the group are spread out from their average value.

3. **Determine if there's a statistically significant difference between the two groups.**
   - This could involve performing a t-test if needed, which compares the means and variances of the two groups to see if the differences are statistically significant.

I'll calculate these steps now.### Results:

1. **Mean (Average) Words Learned:**
   - **Group A:** \( 10.29 \) words
   - **Group B:** \( 10.00 \) words

2. **Variance of Words Learned:**
   - **Group A:** \( 5.24 \)
   - **Group B:** \( 4.67 \)

3. **Standard Deviation:**
   - **Group A:** \( 2.29 \)
   - **Group B:** \( 2.16 \)

### Interpretation:
- **Mean Comparison:** The average number of words learned by Group A is slightly higher than that of Group B.
- **Variance & Standard Deviation:** Group A has a slightly higher variance and standard deviation, indicating that the data points are more spread out compared to Group B.

If you want to determine if this difference is statistically significant, a t-test could be performed.

Would you like further details or have any other questions? Here are some additional questions you might find interesting:

1. How do you perform a t-test to compare these two groups?
2. What does it mean if the t-test shows no significant difference?
3. How can you calculate the confidence interval for the mean?
4. What are the implications of different variances between the two groups?
5. How does sample size affect the comparison of means?
6. How would you graphically represent this data?
7. Can the median be more informative in some cases compared to the mean?
8. How does the range of data compare to variance and standard deviation?

**Tip:** Standard deviation is a key measure to understand the spread of your data around the mean; it is especially important when comparing different groups.

Learn how to compare two groups using statistical measures such as mean, variance, and standard deviation. This problem involves analyzing the number of words learned by two groups after a study session. Includes step-by-step calculation of mean, variance, and interpretation of results. Suitable for advanced high school students and beyond.

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