Does the calculation of average work for negative numbers?

1 Answer

Yup

Explanation:

Let's work a small example: the average of #-1# and #-3#:

#(-1 + (-3))/2=-4/2=-2#.

Now that we've worked out if average can be negative, is there any meaning that can be found in an average negative number.

My answer is that there is, given we have a convention where the negative means something useful.

For instance, if I were to take the average net income for a company that has been losing money over the past two years, there could be a meaning (ex. In year 1, the company lost 1 million dollars (expressed as #-$1,000,000#. In year 2, it lost 3 million dollars (#-$3,000,000# dollars). The average loss for the two years is 2 million dollars, which I can express as #-$2,000,000#.

What if we have a mixed set of numbers, both positive and negative? We do the same thing:

#(-2 + 4)/2=2/2=1#

If we put millions behind this example, we can change the story of the company to say that in year one it lost 2 million dollars but in year two they made 4 million dollars, and so the average income the company made over the two years is 1 million dollars.