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The differences between variance and covariance

Variance is the measure of depression which shows how much numbers in a specific set possibly make a difference from the mean of values. The variance shows the average square of deviations which we have taken from their means. Squaring of deviation is an integral step that will determine the solution of equations. When we […]

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Davis Gibbs

Variance is the measure of depression which shows how much numbers in a specific set possibly make a difference from the mean of values. The variance shows the average square of deviations which we have taken from their means. Squaring of deviation is an integral step that will determine the solution of equations. When we have taken the square of deviation it will ensure that the positive and negative deviations will not cancel each other out. We have calculated the variance in sample and population. 

What is the sample variance?

The population is very large and consists of many entities. It is very difficult to count every value from the population. Hence preferably samples are taken from the population. The sample shows us the average of the population. It consists of the values with manageable size and the data in it is used for calculation. Sample variance is calculated by using the following variance formula:

Sample Variance: Simple Definition, How to Find it in Easy Steps ...

What is population variance?

Population variance σ2 shows us the appointment of data in a specific population that is evenly spread. The calculation of population variance focuses on the average or mean value of distances in the population taken from each data point to mean square. Population variance is calculated by the following variance formula:

VARPA Function in Excel - DataScience Made Simple

Variance calculation is vital for probabilistic and statistical purposes. It helps in finding the results simply and more easily. Variance carries the specific properties firstly, it never shows the negative results because it involves squaring and when the values have squared the results will either be positive or zero. And variance has squared units.

You can use the above formulas to calculate variance in sample or population. But if you are confused you can practice by using the variance calculator. 

What does it mean by the term “co-variance”?

Covariance is an important term that measures the relationship between two different variables (X, Y). These variables are different if there signs it may be positive or negative. 

When the variable is negative it reflects the negative relationship. As covariance definition elaborates, in statistics and mathematics, the measurement of the relationship between two random variables (X, Y) is called covariance.

These variables are either positive or negative numbers and denoted by

Cov(X, Y)Cov(X, Y)

The positive value indicates the positive relationship and it shows that each variable from two tends to move in a similar direction. Whereas the negative value indicates the negative relationship and represents that each of the two variables moves in the opposite direction.  

What is the covariance formula?

VARPA Function in Excel - DataScience Made Simple

The above formula is used to calculate the covariance. The final result will show the covariance between the two different changeable variables X and Y. 

In the above formula, 

cov(X, Y) shows the covariance between two variables X and Y. whereas “x and y” are the components of X and Y. And “n” shows the number of members.

Unlike variance, it can be positive, negative, or zero. The covariance will be zero if the given values do not vary together.  

What is the difference in variance and covariance?

  • Covariance is the measurement of the directional relationship in two different variables, while a variance shows the spread of data which is specifically taken and it is spread around the mean value. 
  • Variance is widely used in probability calculations. This term is used by the financial experts as it is important to count the asset’s volatility. In contrast, covariance throws light on the return throughout two different investments. This is done by comparing different variables.
  • The investors prefer to purchase the investments that have a negative covariance.
  • Variance only tells us the magnitude of how much a quantity will vary concerning its mean. And the magnitude will depend on the data which is spread around mean value. 
  • Despite the magnitude, covariance will show the direction by which two quantities vary or make a difference with each other. 
  • The covariance formula is easy to apply in equations. If you find difficulty in the manual calculation you can also use the covariance calculator. Both variance and covariance are equally important in statistical and algebraic calculations. 

There are online tools like covariance calculator online & variance calculator which can be used to save time & fasten learning.

Math becomes difficult when you try to memorize it instead of learning

Hamza Haroon

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