The variance calculator is used to find the sample and population variance, standard deviation, and mean of a set of data.
The variance is a statistical measure representing the dispersion or spread in a set of data points. It measures how far each element in a data set is from the mean (average) and thus from every other element in a data set. The high variance indicates the more spread out the data points around the mean. It's widely used in statistics, finance, quality control, and many more fields.
The formula for calculating variance is:
S^{2} = 

Where,
s^{2} = Sample variance,
x_{i} = Value of i^{th} element,
x̄ = Mean value of all elements,
n = Number of elements.
σ ^{2} = 

Where,
σ^{2} = Population variance,
x_{i} = Value of i^{th} element,
μ = Mean value of all elements,
N = Number of elements.
To understand the calculation, let's take an example.
Calculate the sample variance for the data set of { 46 69 32 60 52 41 }.
1. Firstly, calculate the mean (average) of the dataset.
Mean (x̄) = (46 + 69 + 32 + 60 + 52 + 41) / 6 = 50.
2. Now subtract the mean from each data point to get the deviation from the mean.
Score  Deviation from the Mean 

46  46  50 = 4 
69  69  50 = 19 
32  32  50 = 18 
60  60  50 = 10 
52  52  50 = 2 
41  41  50 = 9 
3. Square the result.
Squared Deviation 

(4)^{2} = 16 
(19)^{2} = 361 
(18)^{2} = 324 
(10)^{2} = 100 
(2)^{2} = 4 
(9)^{2} = 81 
4. Sum all the squared differences and divide it by the number of data points minus one. That is (n  1) = (6  1) = 5.
Sample Variance (s^{2}) = (16 + 361 + 324 + 100 + 4 + 81) / 5 = 886/5 = 177.22.
Similarly, you can find the population variance using the same method.