Why this formula for 5 year trend? I've opened a spreadsheet that has a 5-year trend formula that I don't understand.
The sample data for $2012$ to $2016$ are: $190, 175, 160, 165, 200$.
The formula in the spreadsheet is:
$trend = 0.1*(-2*190+-1*175+0*160+1*165+2*200)/average(190, 175, 160, 165, 200) = 0.6\%$.
My questions are:


*

*Is this formula standard practice?

*Why are the weights ${-2,-1,0,1,2}$ used?

*Why is the quantity multiplied by $0.1$?

 A: The formula is the linear regression of the series (whatever the variable is), which I will call $y$, on time ($x$), giving units-of-$y$ per year. This is then divided by average $y$ and the result given as a percentage to get a percentage annual growth relative to the mean $y$ (the estimate of the middle-year value of $y$).
Note that the slope of a regression line is $$\hat{\beta}=\frac{\sum_i (y_i-\bar{y}) (x_i-\bar{x})}{\sum_i (x_i-\bar{x})^2}\,.$$ 
Now for the $x$'s being five consecutive years $(x_i-\bar{x})$ will always be $-2,-1,0,1,2$ and $\sum_i (x_i-\bar{x})^2=10$.
At the same time 
\begin{eqnarray}
\sum_i (y_i-\bar{y}) (x_i-\bar{x})&=&\sum_i y_i (x_i-\bar{x}) - \bar{y}\sum_i (x_i-\bar{x})\\
&=&\sum_i y_i (x_i-\bar{x})\,,
\end{eqnarray}
but again the $x_i-\bar{x}$'s are just $-2, ..., 2$ so that's $-2 \, y_1 - 1 \, y_2 + 0 \, y_3 + 1 \, y_4 + 2 \, y_5$.
(Note that $\sum_i (x_i-\bar{x})$ is always $0$, which is why the second term disappeared.)
Consequently the estimated yearly increase using a least squares straight line fit is $\hat{\beta}= (-2 \, y_1 - 1 \, y_2 + 0 \, y_3 + 1 \, y_4 + 2 \, y_5)/10$. This will be in units-of-$y$ per year.
Now to get this to be a yearly relative (or percentage) increase we need to divide by a $y$-value. The mean of the $y$'s, $\bar{y}$ (which is also the estimated middle value in the trend line) is what they've divided by. I don't know why that particular choice was made, rather than some other possible choice --  but for some things I guess this would be a reasonable thing to do. 
I don't know if this is standard, but I bet you could find a formula like this (estimated annual linear increase divided by the mean) in some business stats books or a similar source.
