Standard Deviation (σ) Calculator – Calculate Mean, Variance of Numbers

Standard deviation is the value by which the numbers can be measured in the form of set of data from the mean value, the representation symbol for standard deviation is sigma which is written as σ , another definition for standard deviation of statistics says that it is the measurement of variability of volatility for the given set of data.

The value of standard deviation is directly proportional to the data points or mean value that is if the standard deviation has low value then it will be more closer to the data points and vice versa. We can also say that if the standard deviation has high value then it shows a huge range of different values as the other concepts of maths and statistics says, similarly there are various types of situations where you are freely able to use standard deviation in different kind of questions or equations.

We can also use the concept of standard deviation for the measurement of statistical result which is also the expression for the variability in population like as margin of the error , at this point or set up the another name which is also being used for the standard deviation is standard error of mean or the standard error of estimation in respect of the mean. The calculation of standard deviation allows you to calculate the population standard deviation , the confidence interval approximations and the sample standard deviation.

The standard definition for the standard deviation is also expressed by the population standard deviation which is being used when the complete population is required to be calculated and which is known as the square root of the variance for any given data set like there is any case where all members of a population are taken as sample in such situation we will use the below provided equation for finding or calculating the standard deviation value of entire population.

Formula for Standard Deviation

Now , in the above standard deviation equation we see a sign like reverse Z this sign is known as the summation sign , if you are not aware of it then you will find the above equation a quite difficult to understand but this is not so it is very easy and simple to understand the meaning of this symbol. Although, it might be new for you it is not difficult to understand, the symbol of summation is used at those places where we need to add respective values in large numbers so to gather all of them we use summation sign.

You will see that below this symbol there us a value written as i = 1 which is showing the starting index that means if we are having any set of data like as 1 , 3 , 4 , 7 , 8 then the value of i = 1 is equal to the 1 respective to data set, similarly the value for i = 2 is equal to the 3 because in this set of data at the second place the digit 3 is mentioned in this way we can find the value of i for different positions. So , here we analyze that the notation or symbol of summation is generally meaning that you are needed to complete different operation on every value through N, now as seen in the above-given data set complete value are 5, therefore, the value of N will be equal to the 5.

Sample Standard Deviation Formula

There are various different problems which can occur during any solution like from one of them is a case where we are not able to easily sample each and every member of a population with the help of above equation then at this condition we requires some modification within the equation by which we will be able to easily measure the random sample of population which we are studying. The proper estimation for the standard deviation is basically the sample of standard deviation which is being denoted by the symbol ‘ S ‘.

In the statistics or mathematics there are a various equation which are being used for the calculation of sample standard deviation for example sample standard deviation , sample mean and it do not have any single estimator which is not biased , efficient or have maximum likelihood. The downside provided question is the correct sample for the standard deviation. So, after modification, we got the correct equation of population standard deviation with the use of sample size according to the size of population which is also capable to remove the equation bias , the unbiased estimation which is involved with the standard deviation is unbiased and involved in this situation can vary depending on the distribution.

Standard Deviation ( σ ) Calculator

Now, the next main thing that comes in the field of standard deviation and for which everyone is looking is the standard deviation calculation, till now we come to learn about the standard deviation but the main problem we face is how to find standard deviation and for this calculation we have the standard deviation calculator so we will be going to tell you about this standard deviation calculator and help you in calculating standard deviation. Previously the main work of standard deviation calculators was to only support the direct input and to get after the solution or final result for your calculation but now there has been a lot of modifications occurred in these calculators which allows you to perform various tasks.

The modern standard deviation calculator not only calculate the final result even they also help you to calculate meanmean average, mean statistics and allows you to make different inputs with the help of different kind of methods this modern calculator for calculating standard deviation not only gives the final result it also give you the stepwise procedure or every step of calculation for your better understanding.

So, by this we can easily come to know that this modern standard deviation calculator now are not only limited for the calculation of mean value , variance and standard deviation instead you can even get the stepwise calculation result of your equation. When we try or do calculation manually without using standard deviation calculator for mean or variance calculation the result always vary from one person to another but the calculators give you the exact result without any mistake or error and you will get people result which will not vary with each and every step of calculation. Before going for calculation it is very necessary for you to understand the proper simplicity for the value of your data which we are required at the time of these calculations. In the text file and CSV format input you will be going to get the full detailed step wise calculation for your each question which is being completed by the help of this input method in standard deviation calculator. So , to calculate standard deviation we require the proper formula which we are going to tell you below.

Formula required for calculation

Now, another important thing which comes in our mind is how to calculate standard deviation and for the perfect calculation we need formulas so we are going to tell you the main formulas which are required for calculation purpose like sample standard deviation formula, sample variance formula, mean formula etc. Let us check them out –

There are various different calculators apart from the standard deviation calculator which are very helpful in calculating other important values like variance, sample standard deviation , population standard deviation and much more let us come to know about some of the most used calculators for calculating different values :


1 . Variance Calculator

2 . Sample standard deviation calculator

3 . Population standard deviation calculator

4 . Sample mean calculator

5 . Sample variance calculator

6 . Population variance calculator

7 . Coefficient of variation calculator

8 . Standard deviation calculator excel

9 . Relative standard deviation calculator

10 . Mean standard deviation calculator

11 . Variance and standard deviation calculator

Mean median mode definition

We are studying about the mean, median and mode and it is important to first of all know about the definition of all these :


Mean is also known as the average value for the given set of data in the mathematical term it is also known as the arithmetic mean. For calculating mean we first of all add each and every number given in the data set and then count the number of digits we are having after this simply divide the addition result with the counted number and the answer which you got is known as mean.

For example –

2, 5, 8, 4,

2 + 5 + 8 + 4 = 19 

Now , divide this 19 with 4 because there are total 4 digits.

19 / 4 = 4.75

This resulted value is known as mean.


Median is simply the value of middle digit , in the given date set the middle value is known as median like as in 2 , 5 , 6 , 7 , 4 the middle digit is 6 which is also the median for this data set or if we are not having any single middle term like in 5 , 8 , 2 , 6 , 7 , 8 , 3 there we see total digits are 6 and there is no middle term so we will take 2 middle digits which are 2 and 6 and take the average or mean of these digits like as ( 2 + 6 ) / 2 = 4 , so 4 is the median for this data set.


Mode is very simple to calculate for this we will see those digits which repeating or occurring more number of times in a particular data set. Like we are having the following set of data

2 , 7 , 10 , 15 , 4 , 7 , 10 , 8 , 7 , 2 , 16

In this data set we see that 7 is the digit which is occurring 3 times therefore 7 is telling mode value for this data set.

How to calculate Standard deviation



There are various different ways by which you can easily calculate the standard deviation also you can calculate it practically but here we are talking about the standard deviation calculator by help of which you can easily calculate mean and standard deviation. So , below we are going to give you a stepwise guide by which you will be able to calculate the standard deviation or man for the given set of data with help of this calculator if you also wanted to calculate then follow these below provided steps :

Step – 1 : In the first step you have to find the number of samples from the provided list of data set.

Step – 2 : In the next step you have to calculate or find the sum total for all values individually which are presented in a following set for this calculation you need to follow this formula.

Step – 3 : Now , in this step you will be needed to find or calculate the mean for the given value of data set and for the calculation of mean you are required to follow this formula.

Step – 4 : You are almost at the end of this calculation , here you have to calculate the value of standard deviation and for finding this value you will be going to require the following equation for standard deviation.

Step – 5 : This is the last step in which you will be going to find the value for variance by taking a simple square value for the coming result of standard deviation. So , the variance formula in statistics is simply to get the square root of standard deviation result.

By the help of these above-provided steps you can easily calculate the value of mean and standard deviation or variance , we have also provided the formulas for making your calculation easy. There are many cases in which we need or prefer to calculate the standard deviation value practically you can do this for small calculations but if you wanted to get an accurate result or have a large set of data for calculation then it becomes important for you to use the online available standard deviation calculator which is very helpful for the bulk input method. With the help of above steps you can also calculate the standard deviation from the mean. There are some points for which you have to take care so have a look over it and take care for them.


Noted point :

1 . The value of standard deviation can only be calculated for the real numbers not for any other number like whole or fractional.

2 . The calculation of standard deviation or from the sigma can also be used for the analysis of statistical data.

3 . If you find a result in which the value of signature is very low and also close to the resulted mean value then this simply indicates that the calculated value is accurate and correct.

4 . If you see that the resulted value of signature is high then it shows that your calculated value is not correct or precise.


This was the way in which you can calculate the value of standard deviation with help of online calculators now we will come to know that how can we calculate the mean and standard deviation with excel. So , for this you have to follow the below method :

How to calculate median in Excel or mean 

In this article above we come to know about the formula for calculating mean but now , we are going to tell you that how can you calculate the mean in excel look below for the result calculation.

For it you have to first of all open the Excel spreadsheet in which from the list of column just simply enter a score in one of the column as shown in below image. After entering the desired data you are needed to place the cursor at that place where you wanted the value of mean or average and then click on the button of mouse. Now , after this click on the formula tab and then select the insert function ( fx ) from here you will see a dialogue box will appear on your screen and then from the statistical category simply select the option of Average and then click on OK.

In meanwhile if you wanted to calculate the value of median then simply select the Median instead of mean and then you will get the result for median and mean for whichever you want. After it you have to select the cell range from the list of numbers which are present in the box of number 1 like if you are having your data in Column A in the row number 1 to 13 you have to enter it as A1 : A13 , you do not even need to type the particular range you can easily move the cursor by selecting first number up to the last number and drag it you will get your range automatically and then after selecting your range simply click on the option of OK present at the bottom right side of box and you will get the value for mean in excel.

Calculate standard deviation in Excel

Above we simply calculated the value for mean or median in Excel now we are going to calculate the value of standard deviation in Excel , it is also very simple as above. Same as above first you have to open excel spreadsheet and then simply place your cursor at the place where you wanted standard deviation to be appeared on the screen and then click on the button of a mouse. Now , go to the formula tab and then select the option of insert function ( fx ) and you will be going to see a dialogue box on your screen.

Now, from the statistical category, you are required to select the option of STDEV.S and then make a particular selection of range and then click on the option of OK which is present at the bottom right side of your screen. Next after this you will be required to enter a cell range from the box of number 1 in the available list like as in above example of range or you can also drag the cursor of your mouse from above to down for selecting range and then after this click on the option of OK which is available at the bottom right side of box and then you will get the result for your standard deviation value.

How to calculate variance in excel

For calculating the value of statistical variance in the Excel you need to simply use the function of VAR which is built in feature of Excel. You will be going to get a number of data set from value 1 through the value N so for calculating the value of variance for given data set you will be going to select a cell which is empty in a excel spreadsheet. In the selected cell you have to insert the value in VAR like value 1 , value 2 , value 3 up to value N you can also use the syntax VAR instead of inserting values manually and then select the range like as VAR ( A2 : A18 ) which means from row 2 to row 18.

Next after it you have to select the insert option from tool bar and from which you have to click on the ” function library ” and then after it select the option of insert function and then click on VAR function from the list which appears in front of a screen. Now, select the option of VAR function and after this click the cursor of mouse at the particular place and then select OK from the dialogue box and you will get the value of variance with help of it.

So , by following the above mentioned format you can easily calculate the value for mean , median , variance or standard deviation in excel.

Standard Deviation Graph

When we get lots of standard deviation value sometime we require creating a graph for all those values which makes them more clear and easy to remember. There are many situations in which we needs to make a graph for standard deviation but the main problem we face is that how can we create a standard deviation graph or where to create so , we are here to tell you this. You can easily create a graph of standard deviation in the Microsoft excel of windows and it is very simple to create graph by using different tools available in excel. Here below we are going to provide you a sample graph of standard deviation by the help of which you will get an idea of creating standard deviation graph.

Sample Standard Deviation

So till now we learn about standard deviation and how to calculate standard deviation with standard deviation formula after it we are going to learn about sample standard deviation and how to calculate it. The calculation for sample standard deviation is not that much difficult you just have to follow below mentioned steps :

1 . First of all you have to find out the mean value for the data set which is given to you.

2 . After calculating mean , you have to make a subtraction of mean value from each number present within the data set. Next after subtraction take the square of outcome or result.

3 . Next after this substitute the calculated value in the formula of sample standard deviation formula.

The formula of sample standard deviation is

Standard Deviation Percentage

If you also wanted to calculate the percentage for standard deviation then first of all you have to find out the mean and average for the given set of data without calculating mean and average deviation , next after getting and average value you have to simply divide the average deviation with the mean deviation and then multiply it by 100 and the result which you get will be the standard deviation percentage.

Standard Deviation Example

Till now we have learned about the standard deviation and how to calculate it now, for making the calculation more clear we are going to making it more understandable with help of an example –

Let us assume that we are having the following data set

9 , 2 , 4 , 5 , 7 , 3

1 . We will take the mean of following data set.

( 9 + 2 + 4 + 5 + 7 + 3 ) / 6 = 5

2 . Now , subtract the mean from every value of data set and then take the square of each value.

( 9 – 5 ) ^2  = 16

( 2 – 5 ) ^2  = 9

( 4 – 5 )^2 = 1

( 5 – 5 ) ^ 2 = 0

( 7 – 5 ) ^ 2 = 4

( 3 – 5 ) ^2 = 4


3 . Now , after it you have to simply calculate the mean of these squared values.

( 16 + 9 + 1 + 0 + 4 + 4 ) / 6 = 5.6

This calculated value is known as the sample variance or variance.


4 . Next , for calculating standard deviation we will take the square root of resulted value

√ 5.6 = 2.36


Closure ,

Standard deviation is being used in the history of calculation from a very long time and is being very demanding in different types of fields like measuring the risk which can occur during investment like in stock market , mutual fund , bonds and much more like that you can also use the standard deviation in the field of forecasting weather conditions , pricing of product , digital and analog signal processing etc. If you wanted to make a graph for your values then you can also do this very easily as we also told you this that how can you make the graph of standard deviation in the microsoft excel with help of the various tools available in it so for your better understanding and easy appearance you can use this method of graphing for standard deviation.

With help of Standard deviation calculation you can easily predict the distance for any particular sample in the statistics from any group of mean by a simple calculation of standard deviation. If you also wanted to calculate the standard deviation then you can choose two different ways first one is manual calculation and the another one is with help of an online calculator. There are various online sites which are providing the online calculators for calculating standard deviation so you can easily use any of them. Today in this article we give you all necessary information regarding the calculation and also provided you the stepwise method of calculating the standard deviation.

We tries to tell you each and every information which is related to this subject like sample deviation , variance , mean , median, mode and all hope you will like it and gain some knowledge. Excel is one of the most used  program in windows and the most people wanted to learn how that can calculate standard  deviation or variance in Excel so we also tell you this for calculating and making easier for you. Although you will not face any problem but still if occur then you can contact us simply we will be here for solving all of your problems.