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Difference Between Variance vs Standard Deviation
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. In this article, we discuss the key differences between Variance vs Standard Deviation.
Variance and Standard Deviation Formula
Below is the formula of Variance and Standard Deviation.
Whereas (σ2) is Variance,(X) is (Variable), mean (μ), Total Number of Variables (N).,
Standard Deviation is the square root of the variance.
Example of Variance vs Standard Deviation
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 time.
For Discrete Random Variable the variance is
Where Pi is the Probability of outcome.
The average profit per game for both the cases is Rs.61.54 which game would you like to play well there is a certain instrument that helps to make decision i.e we have to calculate Variance and Standard Deviation
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We need to measure the normal deviation from the expected value 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 tend to followed by large shocks and small shocks in financial assets return tend to followed by small shocks
Variance vs Standard Deviation – Infographics
Here we provide you with the top 6 difference between Variance and Standard Deviation
Variance vs Standard Deviation – Key Differences
The key differences between Variance and Standard Deviation are as follows –
- Variance gives an approximate idea about 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 skewness of the data. Value of skewness of symmetric distribution lies between -1>0>1.
- The geometric mean is more sensitive to variance then Arithmetic mean. Geometric standard deviation is used to find the bounds of the confidence interval in a population.
Head to Head Difference
Let’s now look at the head to head difference between Variance vs Standard Deviation
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 measure the Volatility of Data of a Population | standard deviation, in finance, is often called volatility | |
Variance measure how far the outcome varies from the Mean. | Standard deviation measure 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. | The risk analysis process is the analysis and interpretation of the result collected during the calculation of Standard deviation of various stocks and the result is being analyzed to take an effective decision regarding the investment of funds. |
Use of Variance and Standard Deviation
Example of use of Variance and Standard Deviation in 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 same with market Data of Oil Price.
Final Thoughts
Both Variance and Standard Deviation measures the Spread of Data from its mean point. It helps in determining the RISK in the investment of 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 a been a guide to Variance vs Standard Deviation. Here we also discuss the top difference between Variance and Standard Deviation along with Infographics and comparison table. You may also have a look at the following articles –
- Population Variance Formula | Examples
- Explanation of Sample Standard Deviation Formula
- Explanation of Relative Standard Deviation Formula
- Random vs Systematic Error Differences
- Formula of Sharpe Ratio
- Portfolio Standard Deviation
- Treynor Ratio Calculation
- Sharpe Ratio Excel Examples
- Risk-Adjusted Return Ratios
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