Difference Between Variance and Standard Deviation
Variance is a method to find or obtain the measure between the variables that how are they different from one another, whereas standard deviation shows 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.
Below are the formulas of variance and standard deviation.
- σ2 is variance
- X is variable
- μ is mean
- N is the total number of variables.
Standard Deviation is the square root of the variance.
Imagine a game that works like this
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 /-
- 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 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
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
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 behaviour 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 skewness of the data. The value of skewness of symmetric distribution lies between -1>0>1.
- The geometric mean is more sensitive to variance then Arithmetic mean. A geometric standard deviation is used to find the bounds of the confidence interval in a population.
Variance vs Standard Deviation Comparative Table
|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 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.||The risk analysis 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 take 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.
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.
This has been a guide to Variance vs Standard Deviation. Here we discuss the top differences 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