<PRE><B>Question 368841</B>
Variance is a measure of how far values from a sample or population differ from the mean. &lt;br&gt;

The variance is computed as the average &lt;b&gt;squared&lt;/b&gt; deviation of each number from its mean.&lt;br&gt;

&quot;Squared&quot; numbers are always positive, since a positive number times itself is positive, and a negative number times itself is negative.&lt;br&gt;

And it is obvious that the average of a group of positive numbers must be positive!&lt;br&gt;

For this reason, the variance can NEVER be a negative number.&lt;br&gt;

It can equal zero, but it can never be negative.&lt;br&gt;

In addition, the standard deviation is defined as the square root of the variance.&lt;br&gt;

However, without using imaginary numbers, we can never calculate the square root of a negative number, so again, if the variance is computed to be negative, we have a nonsensical calculation for the standard deviation, as well as for the variance.&lt;br&gt;</PRE>