Coefficient of Variation - Measures of Dispersion, Business Mathematics & Statistics Video Lecture | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

hi welcome to how to stats comm in this
video I'm going to talk about the
coefficient of variation here's the
outline to the presentation what is the
coefficient of variation why is it
useful testing differences statistically
some assumptions and some references so
what is it it's the ratio of the
standard deviation to the mean and this
is the formula so you have the standard
deviation divided by the mean and in
most cases people multiply that
coefficient by a hundred to get a
percentage so as I meant just that
mention a second ago is often expressed
as a percentage so somebody might say
something like the standard deviation is
17% of the mean so that 17% is the
coefficient of variation why is it
useful it's principally useful because
it allows for meaningful comparisons
between two or more magnitudes of
variation even if they have different
means or different scales of measurement
I'm going to give some examples as to
how that's relevant here's one example
where people use or somebody uses the
same measure and as a study by cats at
all where they wanted to examine the SAT
scores under two different conditions
one where as per the test is
administered typically and in another
case where the alternatives to the
answers or the suggested answers or
alternatives are randomized across all
items in the test and they want to see
what people scored when they into two
different conditions so the mean in the
first condition was 54 point 9 and the
standard deviation was 12.1 but in the
randomized condition the mean was 46
point nine and the standard deviation
was ten point eight now what if you
wanted to compare the variability in the
scores between the two conditions
you couldn't just look at the two
standard deviations and say well the
standard deviation is two
point one bigger than this one in a
meaningful way because the mean is also
larger in this case than it is and then
the randomized controls randomized
situation condition so to control for
the differences in the means you divide
12 by 54 and you get a value and you
multiply by the 100 you get a value of
22 so the standard deviation is 22
percent of the mean and in the
randomized condition it's 23 percent so
two values that are actually quite
similar in this case here are twelve
point one versus ten point eight you
might be thinking okay that might be
stitute that might be a fairly
meaningful difference but when you
actually adjust for the fact that they
have different means then the difference
is much smaller here's another example
based on different measures suppose a
researcher wanted to know whether there
was more variability in personality in
comparison to intelligence so here we
have a measure of extraversion we mean
is 50 and a standard deviation of 10 and
for IQ a mean of 100 and a standard
deviation of 15 how would you be able to
compare these two meaningfully to say
whether there's more variability in the
population for personality versus
intelligence well we get the coefficient
of variation in this case it's 20% and
in this case 15 so these results suggest
that there's more variability in
extraversion then there is an IQ even
though the standard deviation is
actually smaller for extraversion but
it's based on a totally different
measure with a different scale so the
only way to make comparisons is with the
coefficient variation now one question
that people often don't ask even though
the coefficient of variation itself