Standard Deviation and Variance Formula, Calculation and Examples

Often students get confused among the standard deviation and variance terms. But in between the two terms, there is a significant difference, and you can get it clear by going through the content below about it all. Standard deviation is usually based on the number which is used to tell about how the measurements for a group are said to be spread out from average or its expected value. The main objective of the deviation is to calculate the central tendency, and as a result, it measures around the mean.

If you take a look at the standard deviation, then you can see that it is beneficial when it compares with the spread of its two separate datasets which is said to have got the approximately of the same mean. If you look at the data set, then you can find that the game which got some small standard deviation has got a narrow spread of measurements that is present around the mean as well as got some high and low values.

When anyone goes for the interpretation, then you can find that the interpretation is quite challenging to consider the data. The mean value size is such that it depends on the size of the standard deviation and it measures in the millions and can measure which are close to the mean value.

What Do you Mean by Variance Definition?

Variance is said to be the measurement of all spread between the numbers in the data set. It measures with each name that is present in the set, and it is taken from the mean. The calculation of the same is done by calculating the difference s that exist between each of the numbers in the set and the way. Then you need to do squaring the differences and divide it with the sum of the squares by the number of values in the set. But it is one of the critical parameters when the allocation of assets comes.

After all these things, the next big question that arises among the students and other people is how to calculate it. Well, these two can help you in a significant manner still you need to apply the right formula when you are going to figure it. To make it easy for you, then you need to follow these simple steps.

How to Calculate Standard Deviation and Variance and Formula?


Here are the steps that are explained in a simple format, and you can get it done quickly.

Step 1:

In the very first step, you need to work out the mean of it. So, when you are putting the formula, then mean of all numbers will be out. It is denoted by mew.

Step 2:

After you have completed the first step, you need to get each number by subtracting the mean and square the result. It is the formula that you need to use when you are going to subtract where x is the individual values, and mew is the result of the mean.

Step 3:

In the next level, you need to add up all the values that you have got. After adding up, you need to divide it by how many, and you need to add up all the values that you get from the previous step. To add up all for getting the sum result, you need to use the Sigma sign. Then you need to add all the values by putting the formula:



But when you have done the above, it doesn’t show the final mean result. But with it, you need to divide, and 1/N does it.

Step 4:

After all this, you need to take the square root of all the things that you have got in the above-stated formulas. So, at last, you can get the final result for your problem.

So, follow these four steps, and you will see that you can solve any problem most straightforwardly.

Properties of Standard Deviation:

The standard deviation has got many properties, and all of it needs to be keep in mind when you are using it in your problem. Here is the list of features that you need to follow.

  • Standard deviation can be used to measure the spread or even can dispersion that is present around the mean of data set.
  • It is very much sensitive to outliers, and it can raise with so much that it can distort all the picture that is present in there.
  • If you ever put the formula, then you can find that standard deviation is never negative.
  • If you look at the data, then the same mean is said to be higher the spread and also higher the standard deviation.
  • If you look at the data set, then it is the standard deviation, which will be zero.

These are the properties of standard deviation, and you need to keep all these in your mind.

What is the standard error?

Many people can’t understand the real mean of standard error. Here is the explanation of all those things in a better manner for you all. The standard error is the relative standard deviation of all statistical sample problem. When you use it, it means that the mathematical term helps in measuring all the accuracy by which a sample can represent a population. If you look at this from a statistics point of view, then the sample means deviates are from the actual mean of the community, and the deviation is only the standard error.


So, with all these things that are mentioned above, it shows that you can take a dig at standard deviation and variance quite easily without much effort. If you have got any doubt about it or how to use the formula for it to find any result then you can go through the article. Here you can get all the details about it simply and transparently and hope it will help you a lot in understanding it.


Author: Naveen E

This is E.Naveen Kumar full time Content Writer, SEO, Digital marketing Expert, founder of Really enjoying playing cricket at free times. Being a Btech Graduation from Computer Science stream Selected full-time blogging as my Profession.

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