Standard Deviation Formula

What is Standard Deviation Formula?

Standard Deviation (SD) is a popular statistical tool that is represented by the Greek letter ‘σ’ and is used to measure the amount of variation or dispersion of a set of data values relative to its mean (average), thus interpret the reliability of the data. If it is smaller then the data points lies close to the mean value, thus shows reliability. But if it is larger then data points spreads far from the mean.

The formula of standard deviation is given below

Standard Deviation Formula 1.1
Standard-Deviation-Formula

You are free to use this image on your website, templates etc, Please provide us with an attribution linkHow to Provide Attribution?Article Link to be Hyperlinked
For eg:
Source: Standard Deviation Formula (wallstreetmojo.com)

Where:

  • xi = Value of each data point
  • x̄ = Mean
  • N = Number of data points
  • Standard deviation is most widely used and practiced in portfolio management services, and 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 portfolio signifies the there is a large variance in a given number of stocks in a particular portfolio, whereas, on the other hand, a low standard deviation signifies a less variance of stock among themselves.
  • A risk-averse investor will only be willing to take any additional risk if he or she is compensated by an equal or a larger amount of return in order to take that particular risk.
  • A more risk-averse investor may not be comfortable with his standard deviation and would want to add in safer investment such government bonds or large-cap stocks in its portfolio or mutual funds for that matter in order to diversify the risk of the portfolio and its standard deviation and variance.
  • The variance and the closely-related standard deviation are measures of how spread out a distribution is. In other words, they are measures of variability.

Steps to Calculate Standard Deviation

Follow the below steps:

  1. 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.

  2. Then, the variance from each data point is measured with the mean it can come as a positive or negative number, then the value is squared, and the result is subtracted by one.

  3. The square of the variance, which is calculated from step 2, is then taken to calculate the standard deviation.

Examples

You can download this Standard Deviation Formula Excel Template here – Standard Deviation Formula Excel Template

Example 1

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

Solution:

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

Standard Deviation Formula Example 1

So, the calculation of variance will be –

Example 1.1

Variance = 0.67

The calculation of standard deviation will be –

Standard Deviation Formula Example 1.2.0

Standard Deviation = 0.82

Example #2

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

Solution:

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

 Example 2

The calculation of mean will be –

 Example 2.1

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

Mean = 10.22

So, the calculation of variance will be –

 Example 2.2

The variance will be –

 Example 2-3

Variance = 15.51

The calculation of standard deviation will be –

Example 2.4

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

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

Standard Deviation Formula Example 3

So, the calculation of variance will be –

 Example 3.1

Variance = 132.20

The calculation of standard deviation will be –

Standard Deviation Formula Example 3.2

Standard Deviation = 11.50

This type of calculation is frequently being used by portfolio managers to calculate the risk and return of the portfolio.

Relevance and Uses

Recommended Articles

This has been a guide to Standard Deviation Formula. Here we learn how to calculate standard deviation using its formula along with practical examples and a downloadable excel template. You can learn more about financial modeling from the following articles –

Reader Interactions

Leave a Reply

Your email address will not be published. Required fields are marked *