sum of errors not 0

#1
I was just looking at some numbers (percentages, if that's useful for this question), and I've been really confused by something: my errors do not sum to zero!

I really do not understand how this is possible - can somebody shed some light on this for me please? Surely if I take each of the following 7 datapoints, subtract it from the mean (x-xbar), and then sum together all of those errors I should be left with 0... But instead I get +- 6.66134*10^-16 (6.66134E-16 in excel).

Numbers:
0.678571429
0.75
0.767857143
0.839285714
0.678571429
0.767857143
0.517857143

(mean = 0.714285714)


Thanks
 

Dragan

Super Moderator
#2
Do not worry, there is not a problem i.e., theoretically, the sum of the values of the deviations of the data points from their mean is still zero. What you are observing is just a very small amount of numerical error in the computation of the sum.

In case you do not know how to read your result, the sum is: 0.000000000000000666134.
 
#3
Do not worry, there is not a problem i.e., theoretically, the sum of the values of the deviations of the data points from their mean is still zero. What you are observing is just a very small amount of numerical error in the computation of the sum.

In case you do not know how to read your result, the sum is: 0.000000000000000666134.
Thanks, that puts my mind at ease!

I have never heard of this before. Would you be able to elaborate a little more? I mean how could there possibly be error in calculating the sum, and what could cause that error?

Thanks