# Standard Deviation

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## Definition of 'Standard Deviation'

In statistics, the standard deviation is a measure of the dispersion of a dataset. It is calculated by taking the square root of the variance. The variance is a measure of how far each data point is from the mean. The standard deviation is often used to measure the risk of an investment.

A low standard deviation indicates that the data points are clustered close to the mean, while a high standard deviation indicates that the data points are spread out more. This means that an investment with a low standard deviation is less risky than an investment with a high standard deviation.

The standard deviation can also be used to compare two or more datasets. A dataset with a lower standard deviation is more consistent than a dataset with a higher standard deviation. This means that the data points in the first dataset are closer to the mean, while the data points in the second dataset are more spread out.

The standard deviation is a useful tool for understanding the distribution of data and for comparing different datasets. It is important to note, however, that the standard deviation does not tell you anything about the shape of the distribution. For example, two datasets with the same standard deviation could have very different shapes.

In finance, the standard deviation is often used to measure the risk of an investment. A low standard deviation indicates that the investment is less risky, while a high standard deviation indicates that the investment is more risky. The standard deviation can also be used to compare two or more investments. An investment with a lower standard deviation is less risky than an investment with a higher standard deviation.

The standard deviation is a valuable tool for investors, but it is important to understand its limitations. The standard deviation does not tell you anything about the shape of the distribution. It also does not tell you anything about the probability of an investment losing money.

Despite its limitations, the standard deviation is a useful tool for understanding the risk of an investment. It is important to use the standard deviation in conjunction with other tools, such as the mean and the variance, to get a complete picture of the risk of an investment.

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