Standard Deviation (Formula and Calculation Steps)

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Standard Deviation

Standard deviation (SD) is a calculation used to measure the number of variations or dispersion within a data set. It can provide an informative overview of how to spread out those numbers. This calculation is important for several reasons, including risk assessment and investing.

This article will discuss standard deviation, the formula for calculating it, its strengths, limitations, and the difference between variance and standard deviation.

What is the standard deviation?

It is a statistical measure of spreading your data. It tells you how different your data is from the average or mean value. It can measure investment risk and compare different data sets.

SD is a useful tool for investors – 

  • It allows them to measure the riskiness of an asset, providing insight into how much volatility they can expect. 
  • High standard deviations indicate that an investment carries higher risks with potentially high rewards than more stable investments, which come with greater certainty and consistency but less reward potential.
  • Although you cannot always depend on standard deviation alone when assessing financial decisions, it provides valuable insights into what outcomes may arise from your choices.

What is the standard deviation formula?

The below formula is to find the standard deviation:

Standard Deviation Formula

How to use standard deviation in different situations?

It can be used in a variety of ways. For example,

  • It can help you compare different sets of data and look for patterns.
  • This will be used to measure the risk associated with an investment, as a higher standard deviation indicates that the range of possible outcomes is greater. 
  • Additionally, it can be used to detect outliers in a set of data.
  • With portfolio managers betting aggressively and taking risks, these investments could yield generous returns.
  • Measuring risk is an integral responsibility for investment firms, and one of the key methods they use to do so is the standard deviation. This metric provides insight into how much a mutual fund or other product fluctuates in value over time – allowing financial analysts, managers, and advisors to make informed investment decisions. 

Tips for effective use of SD

  • When calculating standard deviation, it is important to ensure that your data set is as accurate and complete as possible. 
  • Additionally, looking at the range of values rather than just the mean value can be helpful, as this will give you a greater understanding of how spread out the data is.

How to calculate standard deviation?

  • To find the mean of a data set, add all its values and divide by the number of points. 
  • Calculating variance for each point is determined by subtracting that particular value from the mean.
  • Squaring this variance gives us an indication of how much it deviated from the average.
  • The sum squared variances are then divided by one less than.  
  • Total points to get our final answer–the square root of which reveals just how diverse the entire dataset truly is!
Infographic of How to calculate Standard Deviation

Standard deviation calculator

Many online calculators available can help you quickly and accurately calculate the SD. These calculators are easy to use and will come up with the information you need in seconds.

What does variance mean?

Variance is a way to measure the spread between numbers in any given data set. It’s determined by taking each number, subtracting it from the mean, and squaring that difference – giving us an idea of how much each point differs from all other entries across our entire spectrum.

By understanding variance, we can gain powerful insights into complex sets of information.

Difference between standard deviation and variance

Standard deviationVariance
It can be calculated by discovering the square root of the variance.It is the average difference from the mean.
It shows the spread between numbers in the datasetThe data reveals the contrast between each point and the mean, giving us an insight into how far from average any given situation is.
It will be expressed the same as a unit in the data setIt will be expressed in Squared units or percentages. 


  • The majority of analytics use the standard deviation from investing to actuaries.
  • This is a more accurate, robust statistical measurement
  • The standard deviation of 2 data sets can be merged using a specific formula.
  • This is the only powerful formula to measure dispersion observation.


  • It does not measure how far the data point is from the mean.
  • This can be used for algebraic calculations but is not different from the actual dispersion from the mean.
  • There is a heavier impact of outliers on the SD
  • Manual calculation of SD is very difficult


What does a high deviation mean?

The data observed can be characterized as either widely varied or closely knit groupings based on the size of their standard deviation. If it is high, there is a great deal of dispersion in the observations; if low, most appear to huddle around an average.

What do variance and standard deviation tell?

Variance and SD are powerful indicators of the dispersion of data values from their average. By analyzing them, we can examine how far these numbers strayed from what is normal for that set.


In conclusion, the standard deviation is an important calculation that can be used to measure variation and risk in data sets or investments. By understanding the formula for calculating it and how to use it in different situations, you will be capable of making the best decisions and maximizing your success.

This article discussed the basics of SD and its uses. We also looked at the formula for calculating it and how to use it effectively.

Finally, we discussed why having an accurate SD calculator is important. With this knowledge, you can now use to understand better the data you are working with and make more informed decisions.