To determine which data set has values that cluster closer to the mean, we can compare the standard deviations of the two data sets. The standard deviation tells us how spread out the data points are around the mean. A smaller standard deviation means the data points are closer to the mean, while a larger standard deviation indicates more spread-out values.

• First data set: mean = 8.9, standard deviation = 1
• Second data set: mean = 8.9, standard deviation = 2

Since the first data set has a smaller standard deviation (1 compared to 2), the values in the first data set cluster closer to the mean.

Would you like further clarification or details on standard deviation?

Here are some related questions to explore this topic further:

1. How do you calculate the standard deviation for a given data set?
2. What is the relationship between variance and standard deviation?
3. How does a higher standard deviation affect the shape of a data distribution?
4. Can a data set have the same mean but different standard deviations? Why?
5. In what real-world situations might you prefer a smaller or larger standard deviation?

Tip: A smaller standard deviation always indicates less variability in the data set, meaning values are tightly grouped around the mean.