28 PART 1 Getting Started with Biostatistics
which is just another way of summing all the elements, producing 480. But if you
wanted to omit the first and last elements of the array from the sum, you could
write:
G
i
luci,
2
4
This expression says to add up only Gluc2 + Gluc3 + Gluc4, to get 110
125
95
, which
would equal 330.
Gluc
Gluc
Gluc
Gluc
i
i
2
3
4
2
4
100
95
125
330
Π works just like ∑, except that you multiply instead of add:
Gluc
Gluc
Gluc
i
i
i 1
5
86 110
95 125
64
7,189,600,000
SCIENTIFIC NOTATION: THE EASY WAY TO
WORK WITH REALLY BIG AND REALLY
SMALL NUMBERS
Statistical analyses can generate extremely large as well as extremely small numbers,
but humans are most comfortable working with numbers that are in the range of 10s,
100s or 1,000s. Numbers much smaller than 1 (like 0.0000000000005) or much larger
than 1,000 (like 5,000,000,000,000) are difficult for humans to comprehend. So for
humans, working with extremely large or extremely small numbers is difficult and error-
prone (as is working with certain humans).
Fortunately, to make it easier on all of us, we have scientific notation, which is a way to
represent very small or very large numbers to make the easier for humans to under-
stand. Here are three different ways to express the same number in scientific notation:
1 23 107
.
or 1.23E7, or 1 23
7
.
e
. All three mean “take the number 1.23, and then slide
the decimal point seven spaces to the right (adding zeros as needed).” To work this out
by hand, you could start by adding extra decimal places with zeros, like 1.2300000000.
Then, slide the decimal point seven places to the right to get 12300000.000 and clean it
up to get 12,300,000.
For very small numbers, the number after the E (or e) is negative, indicating that you
need to slide the decimal point to the left. For example, 1.23e–9 is the scientific notation
for 0.00000000123.
Note: Don’t be misled by the “e” that appears in scientific notation — it doesn’t stand for
the 2.718 constant. You should read it as “times ten raised to the power of.”