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

You are watching: Can variance be negative

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)

where:

**x**: The sample mean

**xi**: The ith observation in the sample

**N**: 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 be**14.7**.

**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 be**36.678**.

**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 as*s*) 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 & Examples**Measures of Dispersion: Definition & Examples**