Question

If two normal distributions each have the same mean, but one has a standard deviation of 1 and the other has a standard deviation of 5, what does that tell you about these 2 distributions?

Answer 1

In comparison to a distribution with a standard deviation of 5, one has a curve with a higher peak. The variability will be greater the larger the standard deviation. It denotes increased variability in a distribution with a standard deviation of 5.

What do you mean by the term standard deviation?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. the curve at the top is more dispersed and has a greater standard deviation than the curve at the bottom, which is more concentrated around the mean and has a lower standard deviation.

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