CHAPTER 2 Overcoming Mathophobia: Reading and Understanding Mathematical Expressions 27
Sums and products of the
elements of an array
This Greek letter ∑ is known in English as capital sigma. Though harmless, ∑
strikes terror into the hearts of many learners as they encounter it statistics books
and articles (not to mention its less common but even scarier cousin Π, also known
as capital pi). Uppercase sigma and pi — namely ∑ and Π — correspond to the
Roman letters S and P, which stand for Sum and Product, respectively. These
symbols are almost always used in front of variables and expressions that
represent arrays.
When you see ∑ in a formula, just think of it as saying “sum of.” Assuming an
array named Gluc that is comprised of the five elements 86, 110, 95, 125, and 64,
you can read the expression
Gluc as “the sum of the Gluc array” or “sum of
Gluc.” To evaluate it, add all five elements together to get 86
110
95
125
64,
which equals 480.
Sometimes the ∑ notation is written in a more complex form, where the index
variable i is displayed under (or to the right of) the ∑ as a subscript of the array
name, like this:
Gluci
i
. Though its meaning is the same as
Gluc, you would
read it as, “the sum of the Gluc array over all values of the index i” (which pro-
duces the same result as
Gluc, which is 480). The subscripted ∑ form is helpful
in expressing multi-dimensional arrays, when you may want to sum over only
one of the dimensions. For example, if Ai,j is a two-dimensional array:
10
15
33
25
8
1
then
Ai j
i
, means that you should sum over the rows (the i subscript) to get the
one-dimensional array: 35, 23, and 34. Likewise,
Ai j
i
, means to sum across the
columns (j’) to get the one-dimensional array: 58, 34.
Finally, you may see the full-blown official mathematical ∑ in all its glory, like
this:
Gluci
i a
b
,
which reads “sum of the Gluc array over values of the index i going from a to b,
inclusive.” So if a was equal to 1, and b was equal to 5, the expression would
become:
Gluci
i
,
1
5