Variance Definition
Variance definition states that “variance measures how the numbers in the given data set are dispersed away from the mean of the data set”. In other words, variance measures statistical dispersion.
Variance Formula
The Variance Equation or variance formula is given by:
Variance “Var(A) = E(A^2) - [E(A)]^2 ”, where “E(A)” is the mean or expected value of “A”. In simple words, Variance formula is explained as square of mean subtracted from mean of square.
Unit of Measurement of Variance
Like any other measurement in Mathematics, variance also has unit of measurement. However, variance does not have a specific unit for itself but it uses the unit of the variable. While calculating variance for any given variable, the units of the variable is also squared and the final result i.e. the variance calculated will have the squared unit of the variable as its unit in the answer. For example, suppose variance is calculated for a variable which is measured in meters, then the variance will have the unit “square meter”.
Properties of Variance
Listed below are the properties of variance:
• Variance is proportional to the data scattered around the mean.
• Variance can be calculated for data set containing any number of values.
• All the data sets cannot be compared visually. In such cases, variance helps us to get the numerical measure of the given data sets using which the comparison of the data sets becomes easier.
• Variance is always a positive number because the squares of both positive and negative number will be a positive number.
• If the variable for which variance has to be calculated is a constant random variable, then the variance for this variable will be zero. The variance will not change if the same constant number is added to all the values of the given variable. If all the values of the given variable are scaled by a constant, the variance of that variable is scaled by square of the same constant.
• Among the various methods of dispersion, variance is preferred in case of correlated and uncorrelated variables due to its property. If there are two independent correlated variables whose variances are calculated, we can see that the variance of their sum is given by the sum of the covariance of the two variables. Similarly, the variance of both the sum of the uncorrelated variables is given by the sum of the variances of the variables. It is similar while calculating the difference too.
Variance definition states that “variance measures how the numbers in the given data set are dispersed away from the mean of the data set”. In other words, variance measures statistical dispersion.
Variance Formula
The Variance Equation or variance formula is given by:
Variance “Var(A) = E(A^2) - [E(A)]^2 ”, where “E(A)” is the mean or expected value of “A”. In simple words, Variance formula is explained as square of mean subtracted from mean of square.
Unit of Measurement of Variance
Like any other measurement in Mathematics, variance also has unit of measurement. However, variance does not have a specific unit for itself but it uses the unit of the variable. While calculating variance for any given variable, the units of the variable is also squared and the final result i.e. the variance calculated will have the squared unit of the variable as its unit in the answer. For example, suppose variance is calculated for a variable which is measured in meters, then the variance will have the unit “square meter”.
Properties of Variance
Listed below are the properties of variance:
• Variance is proportional to the data scattered around the mean.
• Variance can be calculated for data set containing any number of values.
• All the data sets cannot be compared visually. In such cases, variance helps us to get the numerical measure of the given data sets using which the comparison of the data sets becomes easier.
• Variance is always a positive number because the squares of both positive and negative number will be a positive number.
• If the variable for which variance has to be calculated is a constant random variable, then the variance for this variable will be zero. The variance will not change if the same constant number is added to all the values of the given variable. If all the values of the given variable are scaled by a constant, the variance of that variable is scaled by square of the same constant.
• Among the various methods of dispersion, variance is preferred in case of correlated and uncorrelated variables due to its property. If there are two independent correlated variables whose variances are calculated, we can see that the variance of their sum is given by the sum of the covariance of the two variables. Similarly, the variance of both the sum of the uncorrelated variables is given by the sum of the variances of the variables. It is similar while calculating the difference too.
No comments:
Post a Comment