Difference Between Variance and Standard Deviation

Variance helps to find the distribution of data in a population from a mean, and standard deviation also helps to know the data distribution in a population. Still, standard deviation gives more clarity about the deviation of data from a mean.

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Formula

Below are the formulas of variance and standard deviation.

Whereas

  • σ2 is varianceX is the variableμ is meanN is the total number of variables.

Standard Deviation is the square rootSquare RootThe Square Root function is an arithmetic function built into Excel that is used to determine the square root of a given number. To use this function, type the term =SQRT and hit the tab key, which will bring up the SQRT function. Moreover, this function accepts a single argument.read more of the variance.

Example

Imagine a game that works like this:

Case-1

You draw one card from an ordinary deck of cards:

  • If you draw 7, you will win ₹ 2,000/-If you choose another card except 7, you will give ₹ -100 /-

Case-2

  • If you draw 7, you will win ₹1,22,000/-If you choose another card except 7, you will give ₹10,100/-

Assume that you played a game 52,000 times.

For a discrete random variable, the variance is

Where Pi is the probability of the outcome.

The average profit per game for both cases is ₹61.54. Which game would you like to play well? A certain instrument helps to make the decision, i.e., we have to calculate variance and standard deviation.

We need to measure the normal deviation from the expected valueExpected ValueExpected value refers to the anticipation of an investment’s for a future period considering the various probabilities. It is evaluated as the product of probability distribution and outcomes.read more, and one common measure is variance. The variance of Case -1 is much less than that of Case -2, which means that the data in Case -2 spread the average value, i.e., ₹64.54, so the Case-1 Game is less risky than the Case-2 Game.

In finance, we talked about the volatility of stocks, meaning that large shocks follow large shocks in financial assets’ return, and small shocks in financial assets’ return tend to be followed by small shocks.

Variance vs. Standard Deviation Infographics

Let’s see the top differences between Variance vs. Standard Deviation.

Key Differences

The key differences are as follows:

  • The variance gives an approximate idea of data volatility. 68% of values are between +1 and -1 standard deviation from the mean. That means Standard Deviation gives more details.One uses variance to know about the planned and actual behavior with a certain degree of uncertainty. One uses standard deviation for the statistical test to know the relationship between two sets of variables.Variance measures data distribution in a population around the central value. Standard deviation measures the distribution of data relative to the central value.Sum of two variances (var(A + B ) ≥ var(A) + var(B ) .therefore variance is not coherent. Sum of two standard deviations sd(A + B ) ≤ sd(A) + sd(B ), so the standard deviation is coherent. It gives the idea of the skewnessSkewnessSkewness is the deviation or degree of asymmetry shown by a bell curve or the normal distribution within a given data set. If the curve shifts to the right, it is considered positive skewness, while a curve shifted to the left represents negative skewness.read more of the data. The skewness value of symmetric distribution lies between -1>0>1.The geometric meanGeometric MeanGeometric Mean (GM) is a central tendency method that determines the power average of a growth series data. read more is more sensitive to variance than the arithmetic means. One uses a geometric standard deviation to find the bounds of the confidence intervalConfidence IntervalConfidence Interval refers to the degree of uncertainty associated with specific statistics & it is often employed along with the Margin of Error. Confidence Interval = Mean of Sample ± Critical Factor × Standard Deviation of Sample. read more in a population.

Variance vs. Standard Deviation Comparative Table

Uses of Variance and Standard Deviation

Example of determination of oil pricing:

  • What will the oil price be in one year? Not one price estimate. A probability of it being low or highVariations in delays, variation in scrap/repair, variation in-flight hours actual vs. plannedDoes the next value move back to the average, or does it only depend on the last value?Does the next amount of demand move back to average, or does it only depend on the last amount of demand?

A forecasted amount for a number of periods (oil price for 20 months)

*The graph is made by considering one year’s data. However, the data shown in the table is only for 6 months. Therefore, the randomly chosen value may not be the same as market data on oil prices.

Final Thoughts

Both variance and standard deviation measure the spread of data from its mean point. It helps determine the risk in the mutual fund investment, stock, etc. In addition, it is a useful tool used in weather forecasting for temperature variation during the period and in Monte Carlo SimulationMonte Carlo SimulationMonte Carlo Simulation is a mathematical method for calculating the odds of multiple possible outcomes occurring in an uncertain process through repeated random sampling. This computational algorithm makes assessing risks associated with a particular process convenient, thereby enabling better decision-making.read more to assess the risk of the project.

This article has been a guide to Variance vs. Standard Deviation. Here, we discuss top differences, infographics, and a comparison table. You may also have a look at the following articles: –

  • Calculate Population VarianceSharpe Ratio Excel ExamplesStandard Deviation FormulaVariance Analysis Definition