In statistics, the term variance refers to just how spread out worths are in a given dataset.

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One prevalent question students regularly have 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 find out why this is the instance, we should understand exactly how variance is actually calculated.

How to Calculate Variance

The formula to discover the variance of a sample (delisted as s2) is:

s2= Σ (xi – x)2/ (n-1)

where:

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

For instance, expect we have actually the following datacollection via 10 values:

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We can use the adhering to procedures to calculate the variance of this sample:

Step 1: Find the Mean

The expect is simply the average. This turns out to be14.7.

Tip 2: Find the Squared Deviations

Next, we can calculate the squared deviation of each individual worth from the mean.

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

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Tip 3: Find the Sum of Squared Deviations

Next, we deserve to take the sum of all the squared deviations:

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Tip 4: Calculate the Sample Variance

Lastly, we have the right to calculate the sample variance as the sum of squared deviations separated 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 just way that a datacollection have the right to have actually a variance of zero is if every one of the values in the datacollection are the same.

For example, the complying with datacollection has actually a sample variance of zero:

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The intend of the datacollection is 15 and also none of the individual values deviate from the suppose. Thus, the sum of the squared deviations will be zero and the sample variance will ssuggest be zero.

Can Standard Deviation Be Negative?

An even more widespread means to meacertain the spreview of values in a datacollection is to use the typical deviation, which is ssuggest the square root of the variance.

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For example, if the variance of a given sample is s2 = 36.678, then the typical deviation (created ass) is calculated as:

s = √s2= √36.678 =6.056

Since we already recognize that variance is always zero or a positive number, then this indicates that the traditional deviation have the right to 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