# 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 the 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 the population can be sampled then the below-mentioned equation can be used by you for finding the value of the **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.

**Variance Formula in Statistics**