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

The standard value is simply the measuring of numbers in the set of data from it’s mean value. Standard deviation is represented by the symbol of sigma ( σ ). You can also say that standard deviation of statistics is the measuring of variability or volatility of the given data set. As much the value of standard deviation is low, it will be closer to the data points which tends to be the mean. Oppositely the higher value of standard deviation shows the wide range of values.

As similar to the other concepts of maths and statistics there are many situations of different types in which you are able to use the standard deviation with help of differential equations. The standard deviation excel is also used for measuring the statistical results in addition of expressing the variability of the population like margin of the error. When you use this for at, the standard deviation is also called as the standard error of the Calculate mean, or the standard error of estimation with respect to mean. The standard deviation calculation can calculate the population standard deviation, the sample standard deviation, and the confidence interval approximations.

The population standard deviation is the standard deviation definition of standard deviation which is used when the whole population is needed to be measured and it is the square root of the variance of given set of data. If there is a case in which every member of population can be sampled then the below-mentioned equation can be used by you for finding the value of standard deviation formula of the whole population –

If you do not know about the summation sign or do not know the meaning of it then the above equation will look like a very difficult one for you but if you will understand the meaning of summation then it will become very easy , basically summation is not very complicated to understand. The value i = 1 below the summation sign shows the starting index which means that if we have the set of data 1 , 3 , 4 , 7 , 8 then the value of i = 1 will be equal to the 1 , the value of i = 2 will be equal to the 3 and so on. So, the notation of summation which simply means that it is needed to perform the operation of on each value through N, in the case of above equation the value is 5 as there are 5 values of the set of data.

## Sample standard deviation

There are a lot of cases in which it is not easy to sample ye every member in the population which can require the above equation which can be modified so the standard deviation can be measured with the random sample of studying population. The common estimator of how to calculate standard deviation is the sample of standard deviation which is denoted by s. As there are many of the different equations for calculating the same.ole standard deviation as like of sample mean sample standard deviation which is not having the single estimator which is unbiased, efficient and has the maximum likelihood. The question which is provided downside is the corrected sample standard deviation. This is the correct equation which is obtained by the modification of population standard deviation equation by using the size of the sample as the size of the population which also able to remove some bias of the equation. The standard deviation of unbiased estimation is highly involved and will vary according to the distribution.

### Application of the standard deviation

1 . Standard deviation is the one which is used widely in the experimental and the industrial settings test models which are against the real world of data. An example for clearly understanding the application can be to use of this in industries for quality control of some products.

2 . Standard Deviation calculation can also be used for calculating the minimum and maximum value of those products which can fall with text high percentage of time due to some aspects of that product. In such cases when the value falls down below the calculated range then it becomes necessary for making changes to the process of production of that particular product for ensuring the quality control.

3 . We are also using the standard deviation in weather determination for calculating the weather conditions of different regions. Just imagine that there are two cities from which one is at the coast and the other one is in the deep inland which is having the same temperature that is of 75°F. Now, this is just a belief or imagination that both of the cities have the same temperature this can be done only in one situation if you ignore the value of calculating standard deviation and only consider the mean value.

Coastal cities have much more stable temperature because of the regulation of temperature by large bodies of water as water is having the high capacity of heat as compared to the land. This phenomenon makes the water less susceptible for changing the temperature and the coastal areas still remain warm even in the winters and remain cool in summers due to the high amount of energy which is required for changing the temperature of water.

So as result we can say that when the temperature of coastal city has the range in between 60°F to the 80°F for the considered times then the mean value will be 75°F , whether the inland city can have to temperature which ranges from 30°F to the 110°F which results in the same mean maths value that is of 75°F.

4 . Finance section is another area in which the standard deviation is used on a large scale where it is used for measuring the risk of price fluctuations at some portfolio and some assets. In such cases, the use of the standard deviation provides the uncertainty of returns in future for the particular investment. Let us have standard deviation example

If we have to compare the stock A which is having the return value of average 7 % with the standard deviation percentage standard deviation of around 10 % with respect to stock B which is having the same average return but the value of standard deviation for stock B is 50 % then the first stock which is A will be much safe option as compared with the second stock which is B. We can not say that you will get the better investment option with A and will got definitive loss in B but there are high chances of getting large returns ( loss ) of stock B as compared to the A due to the high variation of value of standard deviation.

5 . By , calculating the value of standard deviation is valuable at the time when it is important or necessary to know how far will the typical value of mean can be distributed.

## Standard Deviation (σ) Calculator

The previous standard deviation calculators mostly support the direct input and it allows you to find the result which you will get after solution but the modern population standard deviation calculator support the feature of different inputs by the different methods, it not only gives you the end result it will also tell you the step wise step calculation. These modern Sample standard deviation calculator are not only limited for calculating the mean value, standard deviation, and variance but you can also find the results in such a manner which you can directly write down on your paper.

The stepwise step complete sample mean calculator, standard deviation and tell variance along with the corresponding results which can vary user to user if calculated practically without using the calculator it provides you the accurate answer without any chance of error. It is very useful for you to understand the simplicity of data values which are being used in these type of calculations. Leaving the CSV and the text file format input you are allowed to get the complete step wise step calculation for your every question which gets done through the direct input method by using this standard deviation calculator.

## Features of standard deviation calculator

1 . It gives you the result of your calculation in stepwise step method.

2 . This calculator supports a large number of sets of data with the method of bulk file upload.

3 . This calculator also accepts the format of CSV file.

4 . It also accepts the direct input for you like input by copy-pasting or by typing the input values directly into the box provided to you.

5 . Standard Deviation calculator also accepts the format of text file input.

6 . This calculator does not store or save your data which you have used for the calculation.

Mean: Mean Formula is basically the center value or the expected value of the set of data which is also called as average or arithmetic mean of the data. The main aim of calculating the standard deviation of data is to calculate that how much the values of the individual sample are scattered from the mean value

## Sample Standard Deviation Formula

Here we are going to know about some of the main formulas which are used for the calculation of mean, standard deviation and the population variance calculator value of your data.

Step by step calculation of standard deviation

We are here providing you the steps that how you can easily calculate the standard deviation of the data provided to you. If you also wanted to find it the standard deviation then you just need to follow the below-mentioned steps :

Step – 1 : First of all from the set of data you have to find out the number of samples.

Step – 2 : Now, you need to find out the sum of all of the values individually presented in the set of data but using the below formula –

ni=1 xi = x1 + x2 + x3 + … + xn

Step – 3 : Now , you have to find out the mean value of the data by using this formula –

x̄ = ∑ni=1 xi/n

Step – 4 : Next , you have to find out the value of standard deviation with help of the following formula –

σn-1 = √[∑ni=1 (xi – x̄)2 / (n – 1)]

Step – 5 : Now , you have to find out the variance by simply taking the square of the value that comes in the Standard Deviation.

If you wanted to do the calculation by yourself then you can easily done it by using the above mentioned steps and formula for finding the mean , standard deviation and the variance of the data which is provided to you. But , if you are not interested in doing the manual calculation I not sure about your answer then we suggest you to use the online standard deviation calculator for getting the correct details or if you are having a lot of data of data in huge numbers then in such situation standard deviation is going to help you a lot by its bulk input method.

Noted points :

1 . You can only calculate the value of standard deviation for real numbers only.

2 . Calculation of sigma or standard deviation is used for analyzing the data of statistics.

3 . If the value of sigma is low and very close to the value of mean then it simply means that your calculation is precise or accurate.

4 . If the value of sigma is high then it means that your calculation is less precise.

## Standard Deviation Graph

### Methods available in standard deviation calculator

1 . Direct user input method

The main objective of this method which is direct input method is to find out the value of sample standard deviation for small or less data sets and for getting the step wise step calculation of the input data. By using this method of standard deviation calculator you can directly put up your values of data , but for the large sets of data we suggest you to use the CSV method or either the TXT file method.

For ungrouped data

If you are having the ungrouped data then do this –

1 . First of all copy and paste all of your set of data in the box which is provided for input now you have to verify it just remember that data you have entered contains only real numbers and separated by the commas.

2 . Now , you have to simply click on the button of calculate which is provided below the box for sample mean , standard deviation , variance any value you wanted to calculate step wise step.

3 . Now , wait till the results get loaded note down your result and if you wanted to note down the steps for your remembrance then do this.

For grouped data

If you possess the grouped data then you can follow this –

1 . First of all you need to copy and first the first group of your data set in the box which is provided to you for input. Now , verify and check that your data contains only real number.

2 . Now you have to hit on the button of calculate which h is provided below the box for the value which you wanted to calculate.

3 . Now , you have to wait for some time until the result appears on your screen. Note down this result of your first group of data set.

4 . If you are having more groups then put the value of each group one by one in the input box but copy pasting and note down your result for each group after clicking on the calculate button which is present at the below of input box.

### 2 . CSV file upload method

For ungrouped data

Our main objective is just to calculate the mean , standard deviation and variance for the whole data in same time. The maximum file size for CSV which is supportive is of 2 MB not more than that. So , this calculator of standard deviation has only one column for inputting data that’s why the file size of CSV must not increase more than 2 MB. If there will be any row in the CSV file with empty data then it will be ignored automatically.

1 . You have to validate your CSV file ( .csv file extension ) data and make sure that you file does not contain any non real number. You can put up the column name or data name in the first row or you can also choose the option of skip first row of you do not want it.

2 . Now , the first column data is the main element of the CSV file , it must be the data set or the real number only. You are allowed to take only one column data value for calculating the value of sample deviation of the data. Now , you Abe to customize your CSV file to make the first column as the primary data which is fir calculation to avoid the assumption of the calculator that your first column data is your input data.

3 . Now , you have to select the option of ungrouped data for calculating the value of standard deviation for your all data at same time.

4 . Next you have to select on the option of Yes if you wanted your first row to be ignored otherwise you have to select the option of No .

5 . After it you have to choose your preferred CSV file which contains the data set.

6 . Now , click on the upload button for calculating the Standard Deviation.

7 . You will get your calculated result on your screen note it down . Remember it will not save your data in any means or situation.

For grouped data

You can group up your data on the basis of its nature and can calculate the mean, standard deviation and variance value for the each group of your data set separately. If you upload any grouped or ungrounded CSV file ten it will get sorted and grouped by this calculator on it’s own. So , it is not necessary to group your data separately for calculating the standard deviation for any group data. As we told you earlier the file size of CSV should not exceed than 2 MB. For the grouped data this calculator requires the two columns which can be the group data column for input.

1 . First of all you have to verify your CSV data file and make sure that all of the numbers in file are real numbers except in the first row. You can out up the column name or data name in the first row or you can also choose the option of skip first row of you do not want it.

2 . In the CSV file the first column data should be the set of data and real numbers only and the second column of data should also be of same category.

3 . Now , you have to select the option of grouped data for calculating the value of standard deviation for all of your data at same time.

4 . Now , you have to select the YES option if wanted to ignore the first row otherwise simply select the option of NO.

5 . Next , you have to choose the CSV file which contains data.

6 . Now, click on the upload button for calculating the standard deviation.

7 . You will get your calculated result on your screen note it down. Make it remember that this calculator will not save your data in any means or situation.

### 3 . Text file upload method for calculating the standard deviation

For ungrouped data

The main aim for using this method is to calculate the sample mean , standard deviation and the variance for all of the available dates in one time which is irrespective of whether the data is grouped or ungrouped it doesn’t matter in the TEXT file. The maximum size of the text file should not exceed more than 2 MB. This calculator for calculating the value of ungrouped data requires only one column for inputting data. By default it might be possible that the calculator will assume your data of the first column as the input data for avoiding this problem you have you customize the file for making your first column as the primary column. If any row of the column will contain the empty data in your TXT file then it will get ignored.

1 . First of all you need to validate your Txt file with the .txt file extension and look over that your data does not contain any non real number in it. You can put up the column name or data name in the first row or you can also choose the option of skip first row if you do not want it.

2 . Now , the first column data is the main element of the CSV file , it must be the data set or the real number only. You are allowed to take only one column data value for calculating the value of sample deviation of the data.

3 . Now , you have to select the option of ungrouped data for calculating the value of standard deviation for your all data at same time.

4 . Next you have to select on the option of Yes if you wanted your first row to be ignored otherwise you have to select the option of No.

5 . You should take proper care while you choose the data delimiter.

6 . Next , you have to choose your text file which contains data and upload it for calculating the results of standard deviation , mean or variance.

7 . Next , you will get all of theresultst on your screen for your data note them.

For grouped data

The main aim of using this method is to group your data on the basis of it’s nature and calculate the values of standard deviation , variance and mean of your data set for each group separately. If there is any grouped or ungrouped data in your TEXT file which is going to be upload then it will get sorted and grouped automatically by this calculator on it’s own. So , you do not need to group your data separately. For the grouped data calculation this calculator requires the two columns for input of data.By default it might be possible that the calculator will assume your data of the first column as the input data for avoiding this problem you have you customize the file for making your first column as the primary column. If any row of the column will contain the empty data in your TXT file then it will get ignored.

1 . Now, first of all, you need to verify your data or TXT file and make sure that it contains the only real number and the file should not exceed more than 2 MB in its size. You can skip the first row by using the option of skip first row if it contains any name of the column.

2 . Now, you have to select the option of grouped data for calculating the standard deviation for you while data in once.

3 . Next, if you wanted to ignore the first row of the calculator then you can click on the yes option but if you do not want to ignore the first row then simply click on the option of No.

4 . Now, be careful at the time of choosing the data delimiter.

5 . Next, you have to choose your text file which contains data and upload it for calculating the results of standard deviation, mean or variance.

6 . Next, you will get all of the result on your screen for your data note it down for each and every group of your data set.

### 4 . Standard Deviation Calculator Excel

This calculator does not support the data in Excel file directly. You have to, first of all, convert your Excel file to the CSV file format an then simply follow the same steps of CSV file for calculating the Standard Deviation. If you do not know how to calculate the Excel file in CSV then just follow the below-mentioned steps for the conversation of Excel to CSV :

Step – 1 : First of all you have to open and click on the Excel office button which will be provided at the top left corner of your screen on the file.

Step – 2 : Now , you have to click in the save as option and it will open a new window in front of you for locating your directory , give any name to your file and select the preferred option of file type for saving.

Step – 3 : Now , you have to locate the directory in which you wanted to save your file.

Step – 4 : Now , type the name of your file which you have given recently.

Step – 5 : Next , you have to select the save as type as CSV option.

Step – 6 : Your file will get converted in the CSV file after following the above steps.

Closure ,

The use of the standard deviation is very high and demanded , it is spread in the various fields like for measuring the risks of the investment which you are going to do in stocks , bonds , mutual funds etc. , In the section of finance and accounts , used for forecasting the weather conditions , digital and analog signal processing, pricing of product and much more.

In the statistics you are able to predict the distance of individual sample from the group mean by just calculating the standard deviation value which is very important. When it is needed to measure that how widely the value of the individual sample is in a group vary from the average value at that time this online sample deviation calculator will help you a lot. So , we told you about the standard deviation, mean and variance.

We gives you the formula by which you can manually calculator the value of standard deviation if you want or else if you wanted to use this online calculator then also we give you each and every step of all possible methods of this calculator for making your calculation easy so that you will not face any problem while calculating either mean , standard deviation or variance for your set of data. If still the problem persist then you can contact us we will solve your query and solve your problem. We hope that after reading and following the above-mentioned steps you I’ll not be going to face any kind of problem specially in calculating these important values.