## Difference Between Variance and Standard Deviation

Varianceis a method to find or obtain the measure between the variables that how are they different from one another, whereasstandard deviationshows us how the data set or the variables differ from the mean or the average value from the data set.

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

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For eg:

Source: Variance vs Standard Deviation (wallstreetmojo.com)

### Formula

Below are the formulas of variance and standard deviation.

Whereas

- σ2 is variance
- X is variable
- μ is mean
- N 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 card

- If you draw 7, you will win INR 2000/-
- If you choose another card except 7, you will give INR 100 /-

#### Case-2

- If you draw 7, you will win INR 1,22,000/-
- If you choose another card except 7, you will give INR 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 Rs.61.54. Which game would you like to play well there is a certain instrument that 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 a case -1 is much less than the variance of a case -2, which means that the data in case -2 spread average value, i.e., Rs 64.54, so the Case-1 Game is less risk than the Case-2 Game.

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

### Variance vs. Standard Deviation Infographics

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

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Source: Variance vs Standard Deviation (wallstreetmojo.com)

### 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.
- Variance is used to know about the planned and actual behavior with a certain degree of uncertainty. Standard deviation is used for the statistical test to know about the relationship exist between two sets of variable
- Variance measures the distribution of data 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 Deviation sd(A + B ) ≤ sd(A) + sd(B ) so, 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 value of skewness of symmetric distribution lies between -1>0>1.
- The geometric meanGeometric MeanThe geometric mean is a type of mean that uses the product of values often assigned to a set of numbers to indicate the typical values or central tendency of numbers. This method can be used when there is an exponential change in values.read more is more sensitive to variance than the Arithmetic means. A geometric standard deviation is used 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

Variance | Standard Deviation |
---|---|

Average squared differences from mean | The square root of the variance |

Measures Dispersion within the Data Set | It measures spread around the mean |

Variance is not sub-additive | A measure of spread for symmetrical distributions with no outliers. |

Variance also measures the Volatility of Data of a Population. | Standard deviation, in finance, is often called volatility. |

Variance measures how far the outcome varies from the Mean. | Standard deviation measures how far the normal standard deviation is from the expected value. Standard deviation may serve as a measure of uncertainty. |

In Finance, it helps to measure the actual deviation of performance from the standard. | Standard Deviation is a useful tool to take a decision regarding the investment in Stocks, Mutual Funds, etc. because it measures the risk associated with the Market Volatility. |

Corrective measures can be taken by knowing the Variance. | Risk analysis refers to the process of identifying, measuring, and mitigating the uncertainties involved in a project, investment, or business. There are two types of risk analysis – quantitative and qualitative risk analysis.” It process is the analysis and interpretation of the result collected during the calculation of the standard deviation of various stocks, and the result is being analyzed to make an effective decision regarding the investment of funds. |

### Uses of Variance and Standard Deviation

Example of Determination of Oil Pricing

- What will Oil Price be in one year? Not one price estimate. A probability of it being low or high
- Variation in delays, variation in scrap/repair, variation in-flight hours actual vs. planned
- Does the next value move back to 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 the data of one year; however, in the table, the data shown is only for 6 months, and the value is randomly chosen, which may not be the same with market data of oil price.

### Final Thoughts

Both variance and standard deviation measure the spread of data from its mean point. It helps in determining the risk in the investment of the mutual fund, stock, etc. It is a useful tool used in weather forecasting for variation of temperature during the period and Monte Carlo Simulation to assess the risk of the project.

### Recommended Articles

This has been a guide to Variance vs. Standard Deviation. Here we discuss the top differences between them along with infographics and a comparison table. You may also have a look at the following articles –** **

- Calculate Population Variance
- Sharpe Ratio Excel Examples
- Standard Deviation Formula
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