Difference Between Variance vs Standard Deviation
Variance vs Standard deviation is the most widely used statistical mathematical concept, but they also play vital roles throughout the financial field which includes the areas of economics, accounting, and investing.
Dispersion is another statistical jargon that indicates the extent to which the samples or the observations that deviate from the measure (which needs to be appropriate) of the central tendency. Measures of dispersion will fall into 2 categories which are
- A relative measure of dispersion and
- An absolute measure of dispersion.
Variance vs Standard Deviation is the 2 types of absolute measure of variability; which describes how the samples or the observations are spread out around the average or the mean. Variance can be interpreted as the average of the squares of the deviations.
Unlike variance, the standard deviation is the square root of the value (numerical) which shall be obtained while one is calculating the variance. Most people contrast these 2 mathematical concepts and we shall discuss the same.
Head To Head Comparison Between Variance vs Standard Deviation (Infographics)
Below is the top 7 difference between Variance and Standard Deviation
Key Differences Between Variance vs Standard Deviation
Both Variances vs Standard Deviation are popular choices in the market; let us discuss some of the major Difference Between Variance vs Standard Deviation
- Variance is the numerical value that will describe the variability of the individuals or the observations from its arithmetic average of the mean. On the other hand, Standard deviation is another measure of the dispersion of the individuals or the observations within a given set of data.
- Variance, as stated earlier, will measure how far the individuals or the observations in a group or sample are spread out. On the flip side, Standard Deviation will measure how much the individuals or the observations of a given data set differs from its arithmetic average or the mean.
- Variance can be denoted or label by sigma-squared (σ^{2}) whereas the standard deviation can be denoted or labeled as sigma (i.e. σ).
- Variance, as stated earlier, is nothing but an average or the mean of the squared deviations. On another hand, the standard deviation will be the root mean or average squared deviation.
- Variance is always expressed in the square units and which are generally larger or say greater than the values of the observations or the individuals in the given set of data. As opposed to the variance, the standard deviation can be expressed in the same units as the values of the observations or the individuals in the given set of data.
Variance vs Standard Deviation Comparison Table
Below is the 7 topmost comparison between Variance vs Standard Deviation
Basis of comparison |
Variance |
Standard Deviation |
Basic Definition | Variance can be defined as the numerical value which is nothing but the variability of all the observations from its arithmetic average or the arithmetic mean. | The standard deviation can be defined as the measure of the dispersion of the numerical values in a given set of data from their average or the mean. |
Symbol / Label
(in general) |
Variance can be labeled as Sigma^{2} (σ^{2}) | The standard deviation can be labeled as Sigma (σ) |
Usefulness | Variance can help in determining the size of the data spread. | If one wants to measure the absolute measure of the variability of dispersion, then the standard deviation is the right choice. |
What does it indicate? | How far are the individuals or the observations in a group that are spread out? | How many observations or the individuals of a data set differ from its average or the mean. |
Units expressed in | Variance is always expressed in squared units. | The unit of standard deviation is the same as the observations. |
Mostly used? | While deciding upon the asset allocation before investing any of the funds. | Standard deviation can be used to measure the stock market or the stock’s variability either on a daily, weekly, or monthly basis. |
Calculation Methodology | Variance can be calculated by taking the average or the mean of the squared deviation of each of the observations in the data set from its arithmetic mean or average, | One just needs to take a square root of the variance. |
Conclusion
Both Variance vs Standard Deviation is widely common mathematical concepts used in the field of statistics and probability theory as the measures of the variance or the spread. Variance as we discussed is a dispersion absolute measure of how far the observations or the values are actually spread or they vary in a given set of data from their arithmetic average or the arithmetic mean, whereas standard deviation on another hand is a measure of dispersion (again an absolute measure) of the observations or the values that are relative to the average or the mean. Variance can be calculated as the average or mean squared deviation of each observation or the value from the mean in a given set of data, whereas the standard deviation is nothing but simply taking the square root of the variance calculated. The standard deviation as stated earlier is measured in a similar unit as the average or the mean, and to the contrary variance is measured in the squared unit of the average or the mean. Both Variances vs Standard Deviation has its own purpose. Variance is more like a term that is mathematical in nature whereas the standard deviation is mostly used to describe the variability of the given data in a set.
However, there is some identical between them that is both the Variance vs Standard Deviation are always positive. And, if all the given observations in a given set of data are similar or say are identical, then the variance and the standard deviation both will be zero.
These 2 are the most basic statistical terms, which are playing an important role in the various sectors. Standard deviation is mostly preferred over the average or the mean as mentioned earlier it is expressed in similar units as those of the measurements while on the other hand the variance is mostly expressed in the units that are greater or say larger than the given set of the data.
Lastly, these two concepts are used to measure market volatility, which helps in creating a profitable trade strategy.
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