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Which has the larger standard deviation?

What are the mean curves of each of these figures?

To determine which figure has a larger standard deviation, we need to examine how spread out the curves are. The standard deviation of a normal distribution describes how wide the distribution is, or how far the data typically falls from the mean. 

1. **Figure (a)** is more spread out, ranging from approximately 9 to 21, with the mean around 15.
2. **Figure (b)** is narrower, with values ranging from around 3 to 9, and a mean around 6.

Since **figure (a)** is more spread out (it covers a larger range), it has a larger standard deviation compared to **figure (b)**, which is more concentrated around the mean.

### Means of the Figures:
- The **mean** for figure (a) is approximately **15**, as indicated by the peak of the curve.
- The **mean** for figure (b) is approximately **6**, also indicated by the peak.

**Conclusion:**
- **Figure (a)** has the larger standard deviation.
- **The means are:**
  - For figure (a): 15
  - For figure (b): 6

Would you like more details on standard deviation and its role in normal distributions?

### Further Questions:
1. How does the shape of a normal distribution change as the standard deviation increases?
2. What is the relationship between the mean and standard deviation in a normal distribution?
3. Can two distributions have the same mean but different standard deviations? Explain with examples.
4. How does the empirical rule (68-95-99.7 rule) relate to standard deviation?
5. How can we calculate the exact standard deviation from the given graphs?

**Tip:** The larger the standard deviation, the flatter and wider the normal distribution curve becomes.

Understand how to determine which normal distribution has a larger standard deviation by analyzing the spread of two curves. This exercise explores the properties of standard deviation and normal distribution curves, with means of 15 and 6 respectively. Ideal for students in Grades 10-12.

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