https://file.aiquickdraw.com/mathbot/file/1726010554419x53vl87l.jpg

Here are the computed statistics for the two data sets:

- **For data (a)**: [6, 8, 10, 12, 14, 16]
  - Mean: 11.00
  - Variance: 14.00
  - Standard deviation: 3.74

- **For data (b)**: [106, 108, 110, 112, 114, 116]
  - Mean: 111.00
  - Variance: 14.00
  - Standard deviation: 3.74

### Explanation:
1. Both sets of data have the same variance and standard deviation, indicating that their spread or dispersion around the mean is the same.
2. The difference in the means (111 vs. 11) indicates that data (b) is consistently shifted by 100 units compared to data (a).

Would you like further explanation or have any specific questions about the results?

Here are 5 related questions:
1. How does the relationship between the data sets affect the variance?
2. What would happen to the standard deviation if one of the data points in (b) were changed?
3. How is sample variance different from population variance?
4. Why is the mean of data (b) exactly 100 more than data (a)?
5. How would adding a constant to each value in a dataset affect its variance and standard deviation?

**Tip:** When you shift data by a constant (like adding 100), it does not affect the spread (variance and standard deviation), only the mean changes.

Find the mean, variance, and sample standard deviation of each set of data (a: [6, 8, 10, 12, 14, 16], b: [106, 108, 110, 112, 114, 116]) and compare their relationship.

Calculate the mean, variance, and standard deviation for the data sets (a: [6, 8, 10, 12, 14, 16] and b: [106, 108, 110, 112, 114, 116]). Analyze how shifting the data by a constant affects these statistics.

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