Chapter Four!
Calculating a mean
absolute deviation!
On slide thirteen, in Chapter Four, you see that
a mean absolute deviation or M.A.D. "mad,"
is a mean of errors
that are made over a time period without the basis of under or over estimating,
and the formula for MAD
is
the sum
of the actual demands
for a time period
minus the
forecasted
demand for a time period
divided
by "n"
which is the number of time periods we are looking at,
so we're going to be using that
formula
when we take a look
at MAD.
So calculating here we have
our actual
"Demand A,"
our forecasted demand F,
and we want to find the deviation
of that,
A
minus F,
and literally that is just taking
our
demand minus
the forecasted demand. So, a hundred and twenty
minus a hundred and twenty-five is a negative five.
One hundred thirty minus one hundred twenty-five is a positive five.
A hundred and ten
minus a hundred and twenty-five is a negative
fifteen. A hundred and forty
minus
a hundred and twenty-five is a positive
fifteen.
A hundred and ten
minus a hundred and twenty five
is a negative
fifteen,
and a hundred and thirty
minus a hundred twenty-five is a positive
five.
Now, if you notice, we actually took a look
at time periods.
Everything
we worked with was in the same time period,
and there were six separate time periods.
So, to calculate the MAD, remember we said that
our MAD
is the sum of the
absolute value
of A minus F both in the same time period
divided by "n"
so what we want to do is we want to find out what the absolute
deviation is,
and an absolute deviation is the number of clicks on a timeline,
not taking into account whether you are moving right or left, in a positive or
a negative fashion,
but just how many points away. So we literally remove
the sign
and have just the number there, so the absolute deviation of a "negative five"
is five.
The absolute deviation, A minus F
of positive five
is also five.
For the negative fifteen would be fifteen,
for the positive fifteen would be fifteen,
negative fifteen again would be fifteen,
and the positive five would be five. We
removed the positive or negative sign to find that absolute deviation.
We now want to sum
these up because the top
uh... the numerator of our formula
is the sum of A minus F,
So if we add these up, you've got five, ten, fifteen, twenty, twenty-five, thirty, forty,
fifty, sixty.
So the sum
would be sixty and that would be
our numerator.
The "n"
we said was the number of time periods,
and I counted these out onto the side where I put the "t," the one through six - we
have six time periods here, so it would be sixty divided by six,
which is ten.
Now, in and of itself,
that ten means absolutely nothing!
It is a comparison mode, and the smaller the deviation, which means the less your
forecast is away from the actual demand,
the better
the MAD is.
So, if you had a MAD of three versus this MAD of ten
that other way of forecasting would be mimicking what the
actual demand is much better, so that would be a better MAD score or "mean
absolute deviation" score,
but you have to compare
one MAD to a different MAD using two different forecasting methods,
that is looking at
the calculations of mean absolute deviation, or MAD,
and we are now going to move on
to "mean squared error."
"Mean squared error" literally weights, or penalizes, large errors in forecasting
and it is found
by
summing up the "actual" minus the "forecasted" for each time period,
and squaring that, and divide
by "n,"
and that right there is Slide Sixteen
in Chapter Four.
So, if we go to calculate our
mean squared error (MSE),
we're using the same information we had before,
and were going to take
our six-time periods again.
We've already figured out the deviations,
A minus F as a negative five,
five,
negative fifteen,
fifteen,
negative fifteen,
and five,
from our different
time periods,
and we now need to square that.
Now, a negative times a negative is a positive, and I know that seems silly for
me to remind you of that.
But, it's what I call a dummy check.
I am squaring
my negative five,
so negative five times negative five is actually
twenty five,
and I just want to double check myself, that I didn't
mistakenly put
the
negative sign there, that I did do it correctly.
Five times five
is twenty five.
Fifteen
times... or excuse me... negative fifteen times negative fifteen
is two hundred and twenty five, and fifteen times fifteen is two hundred and
twenty five.
I have negative fifteen again,
which is
two hundred and twenty five, and five squared
is twenty five.
Again,
our mean squared
error is found
by summing the "actual" minus the "forecasted" in each time period, squaring them,
divided
by "n."
So, I want to sum
this up.
So, doing it quickly in my head...
one, two, three, four twenty fives,
is a hundred.
Two, three, four, five, six, seven,
with two twenty fives left over, I've got seven hundred and fifty. Always check my
math!
So, my numerator here
is seven hundred and fifty.
Again, I had six
time periods,
so my MSE
is a hundred and twenty five.
Again,
the MSE
cannot
just be taken on its own.
It is a comparative number. You're either going to compare it to an industry standard,
or you are going to compare it
to another MSE (mean squared error) found by a different forecasting
method.
Here, we have a hundred and twenty-five. If the other
MSE that we had was a hundred and eighty two...
this MSE, being a lower number,
would be the better mean squared error, and therefore
the forecasting method would be doing
a better job.
So, that is our mean squared error!