In statistics, the term variance refers to exactly how spcheck out out worths are in a offered datacollection.

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One common question students regularly have actually around variance is:

Can variance be negative?

The answer: No, variance cannot be negative. The lowest worth it can take on is zero.

To discover out why this is the situation, we have to understand also just how variance is actually calculated.

How to Calculate Variance

The formula to uncover 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 implies “sum”

For example, intend we have the adhering to datacollection through 10 values:

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We can use the complying with steps to calculate the variance of this sample:

Step 1: Find the Mean

The suppose is simply the average. This transforms out to be14.7.

Tip 2: Find the Squared Deviations

Next off, we can calculate the squared deviation of each individual value 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 off, we deserve to take the sum of all the squared deviations:

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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 just means that a dataset can have actually a variance of zero is if all of the values in the dataset are the same.

For instance, the following dataset has a sample variance of zero:

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The suppose of the datacollection is 15 and also none of the individual worths deviate from the mean. Therefore, the amount of the squared deviations will be zero and also the sample variance will ssuggest be zero.

Can Standard Deviation Be Negative?

An even more prevalent method to meacertain the spread of worths in a datacollection is to use the standard deviation, which is simply 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 traditional deviation (written ass) is calculated as:

s = √s2= √36.678 =6.056

Since we already understand that variance is constantly zero or a positive number, then this suggests that the conventional deviation deserve 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