# Standard Deviation

Reviewed by Sweta | Updated on Oct 05, 2020

Catalogue

## Introduction

Standard deviation refers to a measure in statistics to find the dispersion in a dataset and its relativity to its mean. The formula to calculate standard deviation is the square root of the variance after obtaining each data point's deviation in relation to its mean. In case the data points are farther from the mean, that means there is a higher deviation in the data set.

## Understanding Standard Deviation

Standard deviation is a statistical measure but widely applied in the finance industry and engineering field, to name a few. In financial measurements, the standard deviation's application is found in obtaining historical volatility in prices or price movements. The results help determine the returns on investment over a period of time.

In the securities market, standard deviation measures the variance between the price and the mean of the prices. The higher the standard deviation, the higher is the variance between the stock prices and the mean of the prices. This, in turn, depicts a wide range of prices. The standard deviation of a volatile stock is high in comparison to a blue-chip whose standard deviation is low.

In the formula for standard deviation, first, we calculate the mean of the data set by adding all the values in the data and dividing it by the number of data values.

Second, we calculate the variance by subtracting each data value from the mean. Then, the results are squared and summed up. The result is divided by the sum of data values less by one. In the final step, the result is squared to find the standard deviation.

Standard deviation is useful in developing trading strategies and also in formulating investing decisions. The volatility of a potential investment or stock is an important factor in investing. Standard deviation helps in measuring the volatility and predicting the likely return on investment.

## Conclusion

Thus, the wider the spread of the data, the higher is the standard deviation. Standard deviation is one of the key measures in assessing the risk by portfolio managers and investment advisors. A high dispersion indicates the high deviation of the return from the expected mean value. However, the standard deviation does not conclude on investment decisions, rather helps understand the data.