The question is asking which of the provided dotplots represents the set of data with the greatest standard deviation.

The standard deviation measures the spread or variability of a dataset from its mean. The larger the spread, the higher the standard deviation. When the data points are more dispersed, the standard deviation is greater, and when the data points are concentrated around the mean, the standard deviation is smaller.

Let’s analyze the options:

• Option A: All the points are clustered together between 0 and 10. This set has a very small spread and will have a small standard deviation.

• Option B: The points are divided into two clusters, one near 0 and one near 10. This shows greater spread, suggesting a larger standard deviation compared to option A.

• Option C: Similar to option B but with more clusters. The spread is still quite large since the data points are spread out from 0 to 10.

• Option D: There are two clusters, but one group is near the middle of the range, reducing the overall spread.

• Option E: The points are more evenly spread out across the entire range, from 0 to 10. This indicates a very large spread, suggesting a high standard deviation.

Conclusion:

The set with the greatest spread is option E, where the points are most spread out across the range, leading to the highest standard deviation.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What is the relationship between variance and standard deviation?
2. How do outliers affect the standard deviation of a dataset?
3. Can a dataset with the same mean have different standard deviations? Why?
4. How do you calculate standard deviation for a sample versus a population?
5. How does the standard deviation change when the entire dataset is shifted by a constant value?

Tip: A larger spread in the data generally results in a larger standard deviation. Look for how dispersed the points are to estimate it visually.