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

hello everybody welcome back to shake
hand in life YouTube channel I am
director Sharma and in this video I will
discuss about the courtesies what is
Tarsus and what are the types of curses
and how would you calculate the curses
for the given data and how would you
identify the kurtosis from the frequency
distribution curve so all these things I
will discuss in this video with you so
stay till the end of this video with me
so that you can understand the the
concept of cutsies completely so
purchase can be used to analyze the data
and thus in the same way skewness and
kurtosis both are what can be used to
analyze the data in the beauty of Six
Sigma in the field of data science and
they are if you are in the field of
statistics then you definitely need to
analyze the data in or the the frequency
distribution curve and for that you have
to analyze the skewness from the
frequency dispersion curve and Persis
also for the frequency distribution
curve
so now come to first we will understand
what is the absolute curses so absolute
curses first understand the Curtis so
Curtis is a measure of the thickness of
the distribution so it is the degree of
measure for that you can understand the
how Pete your distribution whether it is
a less than the normal institution
whether it is the less than peak then
the normal distribution or it is the
higher than the peak of the normal
diffusion so the larger plots lots of
the courses the more peak will be the
distribution when you get the value of
the course is higher you will get the
more peak distribution so Curtis is
calculated and reported either as an
absolute or relative values so courses
can be calculate
either in the posting are either in the
absolutely or in the relative way so it
is depending upon the use of the
courtesy spell you how do you use that
generally the purchase is presented in
the relative format format so absolute
curses is always positive number when we
talk about the absolute courses it is it
it comes as in a positive number and the
absolute course is obtained normal
distribution is 3 and when we talk about
the the absolute value of courses for a
normal distribution curve it is 3 so
here are three types of curve are here
so this is this this is the beat curve
and it is known as the lepto car
t-distribution leptokurtic courtesies
for this description and it is the
normal curve this is the normal curve so
and this is a flatter than the normal
curve so it is platykurtic come and this
is a leptokurtic curve so for the normal
it is also known as the mesokurtic
carbonate now come to the calculation of
the kurtosis
so how do you calculate the cursus the
formula which can be used to calculate
the cursus is this this is the formula
for calculating the cursus and the
measure is beta 2 so beta 2 and this
formula is summation of the all the
individual values the summation of all
these values so this is the summation of
X I minus mu divided by Sigma and for
power of this this operation and then
this divided by the number of
observations so whatever be that number
whatever be the number of the
observations you need to divide all
these this operation divided by the
number of operations you will get the
beta 2 when you now if the beta 2 value
greater than 3 the curve is more peaked
then not normal and it is known as the
laptop guarding curve so here is a
laptop attica in this case the beta
value comes as greater than 3 and in the
second case
the value of beta 2 less than 3 the
curve is less beat and the normal and it
is known as the platykurtic so this is
the case here is the case in this case
the beta 2 value comes as the comes as
less than 3 this is known known as the
platykurtic and if you get the beta 2
value equal to 3 then the curve is
having normal peak in this for this case
and it is also known as mass according
so this case is the meso Critic case for
the normal distribution curve so this
way you can understand the the weakness
of the of the curve and the courtesies
for the frequency distribution now come
to the relative kurtosis basically when
we are talking about the cursus we are
talking about the relative kurtosis now
absolute curtsies as we know that for a
normal distribution is 3 and this value
of 3 is taken as the datum to calculate
the relative curtsies given s so we
consider the 3 as the standard value for
the normal distribution and we take it
as the the datum or a standard value for
calculating the relative kurtosis so
relative courtesies is equal to absolute
vs minus 3 so this is the formula for
calculating the relative courses first
you have to calculate the absolute vs.
then you need to subset 3 from the
absolute curtis's value and whatever you
get you will get the relative
consciousness value relative curses can
be negative in case of absolute cursus
it is always positive value but when we
talk about the relative cursus it will
be negative or positive we always work
with the relative consists and generally
when we are calculating the cursus we
are calculating the cumulative vs. so
courteous means fertility of curses
so this case in this case when the curve
is feet
the value will come as a
Steve Kurtz is positive value and you
will get the positive cut since and you
will get the negative but since in case
of the flatter curve so how would you
calculate the kurtosis we understand
this by an example so we can better
understand the cursus how would you
calculate the courtesies and how would
you identify the courtesies for a
frequency initiation curve and here the
percentage dividend data of 20 different
companies in pharmaceutical sector are
given so dividend data is even here for
20 different companies so the company
some company gives 24% 20 to 14 so hence
the data has given here and how do align
the skewness and courtesies of the given
data so here we are talking about the
skewness we also identify the skewness
and calculating the skewness for this
data but the skewness the video for the
skewness is already available on shaken
like you to Cal and if you want to
understand the concept of students in
detail manner you need to watch the
video of skewness which is available on
my channel shaken with life
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watch them and understand the concept
different concepts of statistics now
come to the this this problem here is
that data values arranged in a different
manner so the data values are arranged
in the Koala Manor so in the first
column you can see here in the first
column you can see here the data is
arranged in the column format and in the
first column
data is available which can be presented
by X I now in the second column we have
already calculated the mean of this data
the mean of this data is twenty-one
point one five and when you subtract
this mean from these individual values
you will get all these data in the
second column
now you also need to calculate the
standard deviation of this data and the
standard deviation of this data is four
point zero seven so how do you calculate
the mean median mode and standard
deviation all these types of videos how
do the calculation of mean the
calculation of median the calculation of
mod and the calculation of standard
deviation all these videos are available
on shaken we'd like you to come and you
can watch all these videos and learn how
to calculate all these these these
statistics measures stretch stick they
just end now come to the this third
column in the third column you have to
divide this these individual values by
extended edition so you will get this
operation X I minus mu divided by Sigma
so all these values comes after dividing
the standard deviation to this this
value and in the fourth column if you
want to calculate the skewness then you
have to take cube of this operation so
that means all of these all of these
individual values need to be cubed so in
the fourth column you will get that cube
of these these values now in the fifth
column what you will get you need to
make fourth power of this disk operation
so in the fourth power of all these
individual values so here you need to
calculate the fourth power of these
these individual values and then sum up
of all these in the fourth column and in
the fifth column and if you want to
calculate the skewness then you
to divide this summation by the number
of observations the number of operations
are 20 and here you can calculate the
skewness value the formula of the
skewness is available in the skewness
with you
and now here we are talking about the
cursus so you need to divide this
summation here is the formula for
curtsies beta-2 and the summation is
divided by the number of observations so
what if we find 1 0 divided by 20 and
you will get 2.15 now you need to
calculate the related curses for radio
courses you have to apply this this
equation absolute curtsies minus 3 and
2.15 is the absolute value and 3 need to
be subtracted from this absolute value
2.1 5 minus 3 and you will get minus
0.85 and what you will find here the
frequency description has left and your
schema swine because the value of
skewness is minus in the negative wave
value and also the radius is also in the
negative
so the skewness is in the description
curve is also in the the left in
readiness and the courses is the
platykurtic means flatter description
and how then the normal distribution and
how view how do we check this whether
these the values
how would you confirm the skewness and
the courtesies from the frequency to
shrink up we can see this in the next
slide so here is a frequency discussion
of the given data
so here the sense in which the frequency
is distributed so intervals class
intervals are there in which the
frequency is of the the number of
companies who given the dividend in
percentage tend to dwell there is no
company who has given the ten to twelve
percent of dividend and 20 to 14 percent
dividend given by the two companies put
into 16 percent of dividend given by the
two companies and so on now the data is
presented by the store robbed here and
in the line graph also so here you can
see that the mean is 20 1.15 median is
22 mod is 24 and the relation is you can
see here the mean is less than medium
and the medium is less than mod so mean
is less than median median is less than
more so this relation is come out when
the curve is left-handed when the
skewness is that left-handed so in the
as we know that the skewness is a
left-handed because the value comes out
in negative and also the it is the
platykurtic curve platykurtic courtesies
because this values the little court
says also comes out as minus 0.85 so in
the you can this way you can understand
from this frequency description what
type of skewness is there in the
frequency distinction and what type of
curses is available in the frequency
description this way you can identify
the skewness and the persists so the
skewness and the persist both are the
important measure to identify the the
disturbance in the frequency to issue in
data and where you need to correct the
data you can identify if you are what in
the field of Six Sigma or you are
working in the field of data science or
you are a student or a teacher of
statistics then this this video is very
important for you you can understand the
concept of both skewness and kurtosis
with this example so this is all about
for this video
very soon I will be available available
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the concept of curses so please do like
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