In statistics, the term variance refers to exactly how spcheck out out values are in a provided dataset.

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One prevalent question students frequently have actually about variance is:

Can variance be negative?

The answer: No, variance cannot be negative. The lowest worth it have the right to take on is zero.

To uncover out why this is the case, we need to understand also exactly how variance is actually calculated.

How to Calculate Variance

The formula to uncover the variance of a sample (deprovided as s2) is:

s2= Σ (xi – x)2/ (n-1)


x: The sample meanxi: The ith observation in the sampleN: The sample size Σ: A Greek symbol that implies “sum”

For example, expect we have actually the following dataset through 10 values:


We deserve to use the adhering to steps to calculate the variance of this sample:

Step 1: Find the Mean

The expect is ssuggest the average. This transforms out to be14.7.

Step 2: Find the Squared Deviations

Next, we deserve to calculate the squared deviation of each individual value from the expect.

For example, the first squared deviation is calculated as (6-14.7)2 = 75.69.


Tip 3: Find the Sum of Squared Deviations

Next off, we have the right to take the sum of all the squared deviations:


Step 4: Calculate the Sample Variance

Lastly, we deserve to calculate the sample variance as the sum of squared deviations divided by (n-1):

s2 = 330.1 / (10-1) = 330.1 / 9 = 36.678

The sample variance transforms out to be36.678.

An Example of Zero Variance

The only means that a dataset have the right to have a variance of zero is if all of the values in the dataset are the same.

For instance, the adhering to dataset has actually a sample variance of zero:


The expect of the datacollection is 15 and also namong the individual worths deviate from the mean. Thus, the amount of the squared deviations will certainly be zero and also the sample variance will certainly sindicate be zero.

Can Standard Deviation Be Negative?

An even more prevalent way to meacertain the spread of values in a datacollection is to use the typical deviation, which is ssuggest the square root of the variance.

See more: How Do You Find Two Unit Vectors Orthogonal To Both (6, 4, 1)

For instance, if the variance of a given sample is s2 = 36.678, then the standard deviation (composed ass) is calculated as:

s = √s2= √36.678 =6.056

Due to the fact that we currently recognize that variance is always zero or a positive number, then this indicates that the typical deviation can never before be negative since the square root of zero or a positive number can’t be negative.

Additional Resources

Measures of Central Tendency: Definition & ExamplesMeasures of Dispersion: Definition & Examples