Standard Deviation and Variance Formula

Hello friends! Standard Deviation and Variance are an important concept in mathematics and statistics. So today through this article we are going to explain you about what is standard deviation and variance, their applications in mathematics and statistics, how to calculate them, etc. Standard deviation is a formula or a tool to measure the dispersion of all the items in a group from the average mean of the group.  Hence it is an important measure to indicate the closeness or distance of the data in the group from the average mean. A low standard deviation indicates that the values in the group are very close to the average mean of the data set. A high standard deviation means that the data is spread out and hence show a lot of variances.

The variance of a data is the square of the deviation

Sometimes, the data might be too large, hence the standard deviation of only a sample or a part of the group might be considered. As students, it is very important for us to understand the concept of standard deviation and variance is to solve statistical problems and understand how “large” or “small”

Standard Deviation and Variance Formula

Standard Deviation and Variance are the two most important concepts in Statistics and Mathematics, hence it is important for the students to understand the concept thoroughly and solve the numerical problems easily. So to help students learn the standard deviation and variance formulas easily, we have provided here with the formulas of both the concepts.

The formula for standard deviation is given below 


For calculating the variance, the following formula is used 

Difference Between Standard Deviation and Variance

Both Standard Deviation and Variance indicate how much spread or how close is the data from the mean value of the data. But if we talk about standard deviation vs. variance, there is a difference between standard deviation and variance. The standard variance is the square root of the variance, while the variance is expressed in square units. Both standard deviation and variance are derived from the mean value of the data. The variance of a particular data set tells us how much each number varies from the average mean of the group. The larger the variance of a data, the greater is the difference between the overall data points in the range.

Hence variance measures how much each data in a group differs from the mean of the given data set. Whereas the standard deviation measures how much the observations of a data set differs from its mean. It is simply the square root of the variance of the data set.

While variance is represented by Sigma-squared (σ^2), the standard deviation is represented by Sigma (σ).

Variance To Standard Deviation Calculator

Sometimes the observations in our data set might be such that the calculations of standard deviation and variance become complicated and it is difficult to get the results. Also, there is a risk of getting the answer wrong. So to make calculations for complex standard deviation and variance sum easier, there is variance to standard deviation calculators which make the calculations for standard deviations and variance easier. So you just have to provide the range of numbers of the data set and press enter to find the values of standard deviation and variance. It is very easy and convenient to use the calculator and it saves a lot of our time and efforts also.

We can use traditional calculators to calculate standard deviation and variance as well. There are special graphing calculators available which allow to enter the values of variables and solve complex equations accurately.

Here we are providing you with a video explaining you easy steps on how you can use the standard deviation calculator.

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