If you have the following measures for two samples:
Sample 1: mean = 15, variance = 7
Sample 2: mean = 7, variance = 15
Which sample has a larger range?

To determine which sample has a larger range, we need to consider the relationship between the range, mean, and variance.

- **Range** is the difference between the maximum and minimum values in a dataset.
- **Variance** is a measure of how much the values in the dataset deviate from the mean.

Generally, a higher variance suggests that the data points are more spread out, which often indicates a larger range. However, the range is not directly calculated from the variance but is influenced by it.

Given the dataTo determine which sample has a larger range, we need to consider the relationship between the range, mean, and variance.

- **Range** is the difference between the maximum and minimum values in a dataset.
- **Variance** is a measure of how much the values in the dataset deviate from the mean.

Generally, a higher variance suggests that the data points are more spread out, which often indicates a larger range. However, the range is not directly calculated from the variance but is influenced by it.

Given the 

- **Sample 1:**
  - Mean = 15
  - Variance = 7

- **Sample 2:**
  - Mean = 7
  - Variance = 15

**Analysis:**

Since Sample 2 has a higher variance than Sample 1 (15 compared to 7), it implies that the data points in Sample 2 are more spread out around the mean. Therefore, Sample 2 is likely to have a larger range.

**Conclusion:**
- **Sample 2** likely has the larger range due to its higher variance.

Would you like more details on the relationship between variance and range, or any other questions? Here are some related questions to consider:

1. How is variance calculated from a dataset?
2. Can a dataset have a large range but a small variance?
3. How is the range calculated directly from data?
4. What is the difference between range and standard deviation?
5. How does variance affect the shape of a distribution?
6. What are other measures of spread besides range and variance?
7. Could two datasets with different variances have the same range?
8. How would changing the mean affect the range?

**Tip:** Remember that while variance gives an idea of the spread of the data, the actual range needs to be calculated directly from the maximum and minimum values.

Explore which sample has a larger range based on mean and variance. Understand the relationship between these statistical measures and their impact on data spread. Example analysis provided for Sample 1 (mean = 15, variance = 7) and Sample 2 (mean = 7, variance = 15).

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