Population Variance Calculator

Online population variance calculator to calculate the variance of data for the whole population. Population variance can be generally derived by dividing the sum of the squared deviation from the mean value. Enter the numbers separated by comma and you get the population variance.

Calculate Population Variance

Result:

Online population variance calculator to calculate the variance of data for the whole population. Population variance can be generally derived by dividing the sum of the squared deviation from the mean value. Enter the numbers separated by comma and you get the population variance.

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Formula: Population Variance Formula Where, σ = Population Variance X = population Data μ = Mean N = Number of Scores

Population variance is defined as the average of the distance from each data point in the population to the mean, squared. It is the measure of how data points are spread out. That is it measures how far each number in the set is from the mean. Population variance, or simply referred to as the variance is calculated by taking the differences between each number in the set and the mean, squaring the differences and dividing the sum of the squares by the number of values in the set. In this online population variance calculator enter the list of population or data separated by a comma and you will get the population variance for the given population or data.

Example

Population Variance

Lets consider x value 4,8,2,9.
Find the mean value to get population varians σ2
μ = (4 + 8 + 2 + 9) / 4
μ = 5.75

Find th sum of difference of population data to the mean and square the obtained value (x - μ)2
4 = 3.0625
8 = 5.0625
2 = 14.0625
9 = 10.5625
∑(x - μ)2 = 3.0625 + 5.0625 + 14.0625 + 10.5625
∑(x - μ)2 = 32.75

Then, dividing by the total value (N)
σ2 = 32.75 / 4
σ2 = 8.1875

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