# How are standard deviation and probability related?

Standard deviation and probability are related in that they are both used to measure and quantify uncertainty or randomness.

Standard deviation is a measure of volatility, which is used to quantify the amount of variation or dispersion in a set of data. It tells us how much the individual data points in a set deviate from the mean of the set.

Probability, on the other hand, is a measure of the likelihood of an event occurring. It tells us the chance of a certain outcome happening, expressed as a number between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event.

In the context of a normal distribution (bell-shaped curve) the standard deviation gives us a way to express the probability that an observation falls within a certain range of values. The normal distribution has a property that 68% of the observations falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

This relationship between standard deviation and probability is very useful in finance and other fields, for instance, it allows risk managers to estimate potential losses in a portfolio of investments, by calculating the probability of different outcomes.

In summary, Standard deviation and probability are related in that they are both used to measure and quantify uncertainty or randomness, Standard deviation measures the amount of variation or dispersion in a set of data, while probability measures the likelihood of an event occurring. In the context of a normal distribution, standard deviation gives us a way to express the probability that an observation falls within a certain range of values. This relationship between standard deviation and probability is very useful in finance and other fields, such as risk management.