Geometric Mean Video Lecture | Mathematics (Maths) Class 11 - Commerce

in this presentation we're going to look
at how to compute the geometric mean the
geometric mean is different from the
arithmetic mean which is the mean we are
quite accustomed to so consider the data
set X which comprises n elements in fact
like the arithmetic mean the fact that
there are n elements is important so
going to make a note of that so we have
the first element second element so on
all the way up to the nth element now
the geometric mean of the data set X is
given as follows this is how you would
denote the geometric mean it is the nth
root
I'll just draw attention out there the N
through so that will be this square root
the cube root the fourth root of all of
the elements of the data set X
multiplied so we actually multiply each
of them together so that's actually
quite a bit of a tricky calculation and
a lot of people like might not be
familiar with how to compute the nth
root so I'm going to show you a slightly
different version so here we have it
there consider the data set X comprised
of the following elements well what we
could do there is again multiply all the
elements out and then put that the power
of 1 over n that's the equivalent of the
nth root but it it's a little bit easier
for people to calculate particularly if
they are not used to calculators right
so let's look at an example here so a
compute the geometric mean of the data
set X now importantly there are five
elements here so N equals 5 and one over
N is not 0.2 so the geometric mean G of
x equals one point zero nine times one
point one one times nine point nine
eight by 1.05
by one point zero one all to the power
of nine point two and we will calculate
that as I'm going to add computer to
four decimal places
that is just bear with me ii have it
written down here at one point two at
five seven four at the power of
knowledge points to and if you're
unfamiliar with how to and calculate
powers look for this little symbol in
your calculator the chevron symbol and
okay so the answer therefore is once we
compute that out we would get an answer
of one point zero four six eight now
again i'm just working to four decimal
places you probably will get a longer
number than that I just decided to work
to four decimal places anyway that is
the geometric mean of the data set X