# Standard Deviation Formula and Uses vs.

Variance. Standard Deviation Formula:

The standard deviation is a measure of how spread out data is. It is calculated by taking the square root of the variance. The standard deviation can be used to calculate the probability that a given data point will fall within a certain range of values.

Variance:

The variance is a measure of how spread out data is. It is calculated by taking the average of the squares of the differences between each data point and the mean. The variance can be used to calculate the standard deviation. What does standard deviation measure in finance? Standard deviation is a measure of volatility in finance. It is a measure of how much a security's price varies over time. A higher standard deviation means that a security's price is more volatile. Does standard deviation measure total risk? No, standard deviation does not measure total risk. Standard deviation is a measure of volatility, which is a type of risk. There are other types of risk, such as credit risk and interest rate risk, that are not measured by standard deviation.

#### What is the relationship between variance and standard deviation?

Variance and standard deviation are two measures of dispersion of a data set. Dispersion is a measure of how spread out the data is. The higher the dispersion, the more the data is spread out.

Variance is a measure of the dispersion of a data set around the mean. It is calculated as the sum of the squared differences between each data point and the mean, divided by the number of data points.

Standard deviation is a measure of the dispersion of a data set around the mean. It is calculated as the square root of the variance.

The standard deviation is a more commonly used measure of dispersion than the variance because it is in the same units as the data. The variance is in squared units.

### Why do we add variances and not standard deviations?

There are two key reasons for this. First, when you are dealing with financial ratios, you are usually more interested in the relative size of the numerator and denominator, rather than the absolute values. For example, when calculating the price-to-earnings ratio, you are more interested in whether the numerator (the price) is high relative to the denominator (the earnings), rather than the absolute values of the price and earnings.

Second, when you add two standard deviations together, the result is not necessarily a meaningful number. For example, if you add the standard deviation of the price of a stock and the standard deviation of the earnings of the same stock, the result is not a meaningful number. However, if you add the variance of the price of the stock and the variance of the earnings of the same stock, the result is a meaningful number (i.e. the variance of the price plus the variance of the earnings).

##### Why is standard deviation The best measure of variability?

There are a number of reasons why standard deviation is the best measure of variability. First, it is the most common measure of variability in the financial world. Second, it is a very reliable measure, as it is based on a large number of data points. Third, it is easy to calculate and interpret. Finally, it is a good measure of the dispersion of data points around the mean.