Question 368841: You figure the variance of a distribution of scores to be -4.26. Explain why your answer cannot be correct.”
Answer by neatmath(302)   (Show Source):
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.
The variance is computed as the average squared deviation of each number from its mean.
"Squared" numbers are always positive, since a positive number times itself is positive, and a negative number times itself is negative.
And it is obvious that the average of a group of positive numbers must be positive!
For this reason, the variance can NEVER be a negative number.
It can equal zero, but it can never be negative.
In addition, the standard deviation is defined as the square root of the variance.
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.
|
|
|
