Standard Deviation Formula Step By Step Calculation

What is Standard Deviation Formula?

The formula of standard deviation is below

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Where:

xi = Value of each data pointx̄ = MeanN = Number of data points
Standard deviation is most widely used and practiced in portfolio management services. For example, fund managers often use this basic method to calculate and justify their variance of returns in a particular portfolio.A high standard deviation of a portfolioStandard Deviation Of A PortfolioPortfolio standard deviation refers to the portfolio volatility calculated based on three essential factors: the standard deviation of each of the assets present in the total portfolio, the respective weight of that individual asset, and the correlation between each pair of assets of the portfolio.read more signifies a large variance in a given number of stocks in a particular portfolio. On the other hand, a low standard deviation signifies less stock variance among themselves.A risk-averse investor will only be willing to take any additional risk if they compensate by an equal or a larger return to take that particular risk.A more risk-averse investor may not be comfortable with his standard deviation. As a result, they would want to add safer investments, such as government bonds or large-cap stocksLarge-cap StocksLarge-cap stocks refer to stocks of large companies with value, also known as the market capitalization of 10 billion dollars or more, and these stocks are less risky than others and are stable. They also pay a good dividend and return, and it is the safest option to invest.read more in the portfolio or mutual funds, to diversify the portfolio’s risk and its standard deviation and variance.The variance and the closely-related standard deviation measure how spread out a distribution is. In other words, they are measures of variability.

Steps to Calculate Standard Deviation

Examples

Example 1

The data points are 1,2, and 3. What is the standard deviation of the given data set?

First, the mean of the observations is calculated just like the average adding all the data points available in a data set and dividing it by the number of observations. Then, the variance from each data point measures the mean. It can come as a positive or negative number, the value is squared, and the result is subtracted by one. The square of the variance calculated from Step 2 is taken to calculate the standard deviation.

Solution:

Use the following data for the calculation of the standard deviation.

So, the calculation of variance will be –

Variance = 0.67

The calculation of standard deviation will be –

Standard Deviation = 0.82

Example #2

Find the standard deviation of 4,9,11,12,17,5,8,12,14.

The calculation of the mean will be –

First, find the mean of the data point 4+9+11+12+17+5+8+12+14/9

Mean = 10.22

The variance will be –

Variance = 15.51

Standard Deviation = 3.94

Variance = Square rootSquare RootThe Square Root function is an arithmetic function built into Excel that is used to determine the square root of a given number. To use this function, type the term =SQRT and hit the tab key, which will bring up the SQRT function. Moreover, this function accepts a single argument.read more of standard deviation.

Example #3

Variance = 132.20

Standard Deviation = 11.50

Portfolio managers frequently use this type of calculation to calculate the risk and return of the portfolio.

Relevance and Uses

Standard deviation is historically helpful in analyzing a portfolio matrix’s overall risk and return. It is widely used and practiced in the industry. The correlation and the weights of the portfolio’s stocks can impact the portfolio’s standard deviation.As the correlation of the two asset classesAsset ClassesAssets are classified into various classes based on their type, purpose, or the basis of return or markets. Fixed assets, equity (equity investments, equity-linked savings schemes), real estate, commodities (gold, silver, bronze), cash and cash equivalents, derivatives (equity, bonds, debt), and alternative investments such as hedge funds and bitcoins are examples.read more in a portfolio reduces the portfolio’s risk, it is not necessary all the time that an equally weighted portfolio provides the least risk in the universe.A high standard deviation may be a measure of volatility, but it does not necessarily mean that such a fund is worse than one with a low standard deviation. For example, if the first fund is a much higher performer than the second one, the deviation will not matter much.Standard deviation is also used in statisticsStatisticsStatistics is the science behind identifying, collecting, organizing and summarizing, analyzing, interpreting, and finally, presenting such data, either qualitative or quantitative, which helps make better and effective decisions with relevance.read more and is widely taught by professors at various top universities worldwide. However, the formula for standard deviation is changed when one uses it to calculate the sample’s deviation.The equation for SD in Sample = just the denominator is reduced by 1.

What is Standard Deviation Formula?#

Steps to Calculate Standard Deviation#

Examples#

Example 1#

Example #2#

Example #3#

Relevance and Uses#

Recommended Articles#