Standard Deviation Calculator: Step By Step guide to calculate the SD manually

 Standard Deviation Calculator: Step By Step guide to calculate the SD manually

The online Calculator available at is an efficient tool for calculating Standard Deviation. With the use of this software, you can easily analyze statistics and compute the standard deviation of a dataset. Standard Deviation is a measure of how spread out the values in a dataset are from the mean. It provides valuable insights into the variability and dispersion of the data. By utilizing the Standard Deviation Calculator from, you can obtain accurate and reliable results, saving time and effort in your statistical analysis. This tool simplifies the process of calculating standard deviation and allows you to focus on interpreting and understanding the variability within your dataset.

These can also be calculated with the help of formulas.

The steps are listed below.

  • Determine the Mean.

You must add all the values and divide them by the total number.
Example.X=1+3+4 ..6/6 =50 

  • Find the SD for every value from the mean.

Subtract the mean from every value to get the Deviation of the mean.

Considering the same values from the example.

As x=50 
46-50= -4, and so on for every value.

  • Square every Deviation derived from the mean 

Multiply Every Deviation by the mean value from the mean. It will determine positive results.


  • Determine the total of the squares.

In this, add all the squared values. Like if there are six values. For every six values, there will be six squared values. Now add all these values together.

For example 

  • Evaluate the Variance 

Now the sum of all the squares needs to be divided by n-1. It is for the Sample or N(Population)

Consider the example.

Since the example has a sample value of 6. Using n-1. Here n=6 

So 886/(6-1)=886/5=177.2 

  • Evaluate the Square root of the Variance calculated/derived.

Now to calculate the Standard Deviation, square root the Variance value.


Since the Standard Deviation value is 13.31, each score deviates from the mean of 13.31.

What does a Standard Deviation determine?

The Standard Deviation is the amount of average variability. Considering the data set determines how close you are to the mean value.In a normal distribution, the SD is higher than the mean. It is far away or scattered from the mean value.
In the case of a lower SD, it means the mean value is closest to the mean value.


The Standard Deviation Calculator can help in huge Calculations related to population and case studies.

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