A:

The standard deviation, or SD, measures the amount of variability or dispersion for a subject set of data from the mean, while the standard error of the mean, or SEM, measures how far the sample mean of the data is likely to be from the true population mean. The SEM is always smaller than the SD.

The formula for the SEM is the standard deviation divided by the square root of the sample size. The formula for the SD requires a few steps.

  1. First, take the square of the difference between each data point and the sample mean, finding the sum of those values.
  2. Then, divide that sum by the sample size minus one, which is the variance.
  3. Finally, take the square root of the variance to get the SD.

The SEM describes how precise the mean of the sample is versus the true mean of the population. As the size of the sample data grows larger, the SEM decreases versus the SD. As the sample size increases, the true mean of the population is known with greater specificity. In contrast, increasing the sample size also provides a more specific measure of the SD. However, the SD may be more or less depending on the dispersion of the additional data added to the sample.

The SD is a measure of volatility and can be used as a risk measure for an investment. Assets with higher prices have a higher SD than assets with lower prices. The SD can be used to measure the importance of a price move in an asset. Assuming a normal distribution, around 68% of daily price changes are within one SD of the mean, with around 95% of daily price changes within two SDs of the mean.

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