Variance Calculator

The variance calculator is used to find the sample and population variance, standard deviation, and mean of a set of data.

Result:

Variance:
Standard Deviation:
Mean:
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How to Use the Variance Calculator?

  1. Firstly, enter the set of values or the data with commas or spaces separated. For example 3 5 7 8 10 or 3, 5, 7, 8, 10.
  2. Select the data type whether it's sample or population.
  3. Lastly, press the 'Calculate' button.
  4. As a result, the tool shows the variance result, standard deviation, and mean.
  5. Press the 'Reset' button to clear all the input and output fields.

What is Variance?

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.

Variance Formula

The formula for calculating variance is:

Sample Variance:
S2 =  
∑ ( xi - x̄ )2
n - 1

Where,
s2 = Sample variance,
xi = Value of ith element,
x̄ = Mean value of all elements,
n = Number of elements.

Population Variance:
σ 2 =  
∑ ( xi - μ )2
N

Where,
σ2 = Population variance,
xi = Value of ith element,
μ = Mean value of all elements,
N = Number of elements.

How to Calculate the Variance?

To understand the calculation, let's take an example.

Example:

Calculate the sample variance for the data set of { 46 69 32 60 52 41 }.

Solution:

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.

ScoreDeviation from the Mean
4646 - 50 = -4
6969 - 50 = 19
3232 - 50 = -18
6060 - 50 = 10
5252 - 50 = 2
4141 - 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 (s2) = (16 + 361 + 324 + 100 + 4 + 81) / 5 = 886/5 = 177.22.

Similarly, you can find the population variance using the same method.