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.