Last time I gave an
example of a model to compute an average.The method I used to compute the average was probably the most familiar
method there is - basically, add up all the number and divide by the count of
the numbers that were added.
This works well on
paper but can lead to problems on computers.One error that can creep in is adding up to a number bigger than the
computer can handle.Humans with pencil
and paper can always make numbers bigger (just add more paper) but a computer
will have the maximum number it can handle.
32 bit computers are
still popular and for this next bit let's assume the largest integer it can
handle is 4,294,967,294. This is the number 2 raised to the 32nd power (2
because the machine is binary, and 32 from the 32 bit processor).Four billion is a large number, but if we are
trying to figure out average sales for a really large business, it won't work.
When we try to add numbers that total to more than 4 billion, the computer will
not know what to do - it can't count that high.
This isn't new: this
is a very old problem with computers.No
matter how you do it, there is a number that will be bigger than the computer
can handle.Just fill up all the computer
memory with whatever number you want (all 1s, since it is binary) and then add
1 more to it.The computer doesn't have
enough memory to hold that new number.
So how can we deal
with this potential problem?
One way is to change
our algorithm.Our original algorithm is
Add all the numbers in the
Divide by the count of the
numbers in the original list
The answer I get is the
result I want
But we can crash at
One workaround is to
look really hard at what the algorithm does.Our example had 5 grades, so we add them up and divide the total by
5.What if we divided each number by 5
to begin with, and then added up those results?
17.6+18.2+16.6+17.6+17=87This was the
output of the original algorithm, so this new algorithm looks like it might be
So the new algorithm
Count the number of items in
Divide the first number by
that count and add the result to a running total
Divide the next number in the
list by that count and add the result to the running total
Repeat step 3 until all the
items in the list have been processed
Seems reasonable and
next up we will give this a try.
concerns and criticisms always welcome,