Answer: True
Explanation:
The term inside the parentheses after the summation sign is
x-sub-i minus x-bar
x-bar is the mean average of all the individual n observations. In statistics, it is usually just called the 'mean' for short.
x-sub-i stands for each individual observation: x-sub-1, x-sub-2, and so on
So that means (x-sub-i - x-bar) means the difference we get if we do the subtraction, using x-sub-i as the first term in the subtraction.
For an illustration of this, suppose we have a sequence of 5 observations. Since there are 5 observations, n = 5.
x-sub-1 = 4
x-sub-2 = 7
x-sub-3 = 3
x-sub-4 = 11
x-sub-5 = 5
We obtain the mean by adding all the observations and then dividing by the number of observations, n.
The sum 4+7+3+11+5 = 30 and 30/5 = 6.
So the mean, x-bar, = 6.
Now let's look at all the differences between each observation and x-bar.
In the same order as the observations, we get
4 - 6 = -2
7 - 6 = 1
3 - 6 = -3
11 - 6 = 5
5 - 6 = -1
If we add up all the differences, just like we are doing in the summation homework problem, we have (-2)+1+(-3)+5+(-1) = 0.
It also works if you make x-bar the first term in the subtraction. Either way will work, as long as you are consistent about it from one subtraction to the next.
This is always the case with a mean average, so the summation is assured to be zero.
I hope this helps.