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In order to explain anything useful about statistics we have to use some sort of algebraic notation. This does not imply you have to be able to 'do' algebra - you just need some idea of what the various symbols are about - and how they tend to go together. Unfortunately, despite what mathematicians may tell you, these symbols are anything but standardized - and all manner of abbreviated notation is in common use. To avoid a great deal of unnecessary suffering - let us 'bite the bullet' and describe one of the most common types of notation using a very familiar statistic.
The mean () (pronounced 'y bar') is commonly written as
To keep us in touch with reality, let us define variable Y as milligrams of active ingredient (a.i.) per ml of a dewormer - assayed in our laboratory. Let's say we take seven samples of the dewormer. Each of these can be considered as a separate observation, or replicate:
Then we could describe each observation of variable Y like this:
To save space we can abbreviate this list of observations to Y1, Y2, Y3, ... Yn
So the 'sum of Y' is Y1 + Y2 + Y3 + ... Yn
Alternately, if you wish to be explicit, you could write this as: Σ(Y1, Y2, Y3, ... Yn)
Where i stands for observation numbers 1 to 7, in our current list of (n) measurements. The subscript (the expression below Σ) and the superscript (the expression above sigma) indicate the first and last items to be included in the sum.
We can abbreviate the above formula in various ways.
Let us use the simplest of these notations.
In this case Σ Y = 749 for n = 7 observations