Variance and Standard Deviation

What Does Variance Mean?

Variance is defined as the statistical measurement which determines how far each number is from the mean value in a given data set. It tells us about the degree to which our average value can deviate in the data set.

What Does Standard Deviation Mean?

Standard deviation is the measure of the volatility from the mean value in the given data set. It is calculated by taking the square root of the variance of the given data set. It calculates the risk related to the change in values in the market.

What Is the Difference Between Standard Deviation and Variance?

Variance is calculated by taking the average of the squared deviation from the mean, whereas standard deviation is the square root of the variance. The other difference between them is in their unit. Standard deviation is expressed in the same units as the original values while Variance is expressed in unit².

What is Variance formula?

Formula to calculate the variance of the given data set is,

σ² = Σ (x_i – x̅)²/n

What is Standard Deviation formula?

Formula to calculate the variance of the given data set is,

σ = √(Σ (x_i – x̅)²/n)

Does standard deviation have units?

As standard deviation tells us about the volatility of the data thus It has the same unit as the data in the given data set.

Variance and Standard Deviation are the important measures used in Mathematics and Statics to find the meaning from a large set of data. The different formulas for Variance and Standard Deviation are highly used in mathematics to determine the trends of various values in mathematics. Variance is the measure of how the data points vary according to the mean while standard deviation is the measure of the central tendency of the distribution of the data. 

The major difference between variance and standard deviation is in their units of measurement. Standard deviation is measured in a unit similar to the units of the mean of data, whereas the variance is measured in squared units.

Here in this article, we will learn about variance and standard deviation including their definitions, formulas, and their differences along with suitable examples in detail.