Geometric Mean - Measures of Central Tendency, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com

all right in this video I just want to
do a quick little example about the
geometric mean and also to point out you
know what kind of how you can think
about it what it means
so the definition the geometric mean of
two numbers a and B what we do is we
multiply those two numbers together and
then we take the square root of them and
that's the geometric mean so certainly
not the same as the arithmetic mean the
average I think that's the one most of
us are certainly more familiar with so
let's look at a simple example here
let's find the geometric mean of 4 and 9
so again what we'll do is we'll multiply
those two numbers together and then
we'll simply take the square root of
those so 4 times 9 well that's going to
give us 36 so we have to take the square
root of 36 well that's simply equal to 6
so we would say that the geometric mean
of the numbers 4 & 9 the geometric mean
is going to equal 6 so you know what
what is what's special about the
geometric mean I guess you know again I
think an average an arithmetic mean it's
kind of the middle point right and I
think you know people you know you find
an arithmetic mean if you want to find
for example your average grade on two
tests so you know what is this number
six represent in relation to four and
nine well what it has to do with it has
to do with ratios okay so we started
with four and nine those were the
numbers that we are finding the Aerith
excuse me the geometric mean of and we
found that geometric mean to equal six
well notice if we look at the ratio four
divided by six and then if we look at
the ratio 6 divided by 9
well 4 over 6 reduces to 2/3
hey 6 over 9 also reduces to 2/3 so this
is kind of what's special about this
number the geometric mean if you take
the ratio of the small number to the
geometric mean and then if you look at
the ratio of the geometric mean to the
larger number those ratios or those
fractions are going to be the same
okay so that's that's that's how you can
kind of think about the geometric mean
somehow it's giving equal ratios of
those two values so again the arithmetic
mean is the one that I think most of us
a little bit more used to so again just
to refresh you the arithmetic mean we
would just add those two numbers
together you know 4 plus 9 and then
divide by 2 I guess four plus 9 that's a
13 over 2 and 13 divided by 2 I believe
that's going to give us what 6.5 okay so
the arithmetic mean is 6.5 the geometric
mean was 6 and this leads to one other
last little remark without a proof but
it turns out that the geometric mean is
always less than or equal to the
arithmetic mean okay
so one other little useful results so
again if you want to find your average
grade on two tests you're not going to
use the geometric mean you're going to
use the more familiar arithmetic mean
but the geometric means certainly does
show up and again I think it's something
that people most people are familiar
with I certainly wasn't for a long time
so just in case you see it that's all
there is to it and that's it again it
just really has to do with making ratios
equal to each other