Understanding Standard Deviation: Comparing the Spread of Two Normal Distributions

Consider the following three distributions.Of the two normal​ distributions, which has the larger standard​ deviation?

To determine which of the two normal distributions has the larger standard deviation, we need to compare the spread or variability of the data in each distribution

To determine which of the two normal distributions has the larger standard deviation, we need to compare the spread or variability of the data in each distribution.

Standard deviation measures how spread out the values of a dataset are from the mean. A larger standard deviation indicates greater variability, whereas a smaller standard deviation indicates less variability.

Without specific values for the means and standard deviations of the two normal distributions, we cannot make a direct comparison. However, we can still discuss the relationship between standard deviation and the shape of a normal distribution.

In a normal distribution, the spread is determined by the standard deviation. If the standard deviation is small, the values are concentrated closely around the mean, resulting in a narrow and tall bell curve. Conversely, if the standard deviation is large, the values are spread out further from the mean, resulting in a wider and shorter bell curve.

Based on this information, if one normal distribution has a narrower and taller bell curve compared to the other, it implies that the former has a smaller standard deviation while the latter has a larger standard deviation.

In summary, to determine which of the two normal distributions has the larger standard deviation, we would need specific values for the means and standard deviations. However, by comparing the shapes of the distributions, a wider and shorter bell curve suggests a larger standard deviation.

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