document.write( "Question 368841: You figure the variance of a distribution of scores to be -4.26. Explain why your answer cannot be correct.” \n" ); document.write( "

Algebra.Com's Answer #262770 by neatmath(302) $\"\"$ $\"About$

You can put this solution on YOUR website!
Variance is a measure of how far values from a sample or population differ from the mean.
\r
\n" ); document.write( "\n" ); document.write( "The variance is computed as the average squared deviation of each number from its mean.
\r
\n" ); document.write( "\n" ); document.write( "\"Squared\" numbers are always positive, since a positive number times itself is positive, and a negative number times itself is negative.
\r
\n" ); document.write( "\n" ); document.write( "And it is obvious that the average of a group of positive numbers must be positive!
\r
\n" ); document.write( "\n" ); document.write( "For this reason, the variance can NEVER be a negative number.
\r
\n" ); document.write( "\n" ); document.write( "It can equal zero, but it can never be negative.
\r
\n" ); document.write( "\n" ); document.write( "In addition, the standard deviation is defined as the square root of the variance.
\r
\n" ); document.write( "\n" ); document.write( "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.
\n" ); document.write( "

\n" );