Free Hand Curve Method, Business Mathematics and Statistics Video Lecture - Business Mathematics and Statistics - B Com

hello and welcome to another session of
annotated technique videos at HPD of
WorldCom your most favorite portal for
online education in our previous session
we started with the time series analysis
and we had seen its definition its
components and what basically is time
series analysis and how it has done this
session we shall move on with the same
topic that is time series analysis and
we'll see the measurement of various
components to begin with
we'll start with the measurement of
secular trend we have different methods
of measuring trend and some of the
principal methods are given below the
simplest the easiest method is the
graphical or freehand curve method then
we have the method of averages under
which we have the method of selected
points we have the method of semi
averages and we have the method of
moving averages further we have the
mathematical trend under which we have
the method of least square and by using
the method of least square
apart from fitting the linear trend we
can also fit parabolic or exponential
trend we will only be seeing the linear
trend for now and so we will basically
be looking at the graphical method all
the three method of averages and in the
method of least square we will use the
setting of linear trend for now in this
session we will begin with the graphical
method move on with the method of
averages and see the first two method of
averages that is the method of selected
points and the method of semi averages
in the subsequent videos we will see the
moving average and the linear trend
methods
so let's begin with the graphical method
graphical method is the simplest method
to study the trend here the time series
data is plotted on a graph by taking the
time on the x-axis and the other
variable on the y-axis a smooth line or
curve is drawn through the plotted
points which would represent the trend
of the given data very simple we will
take an example we will see a numerical
example and understand how this plotting
is done well here we have a data where
we see that we have the data of 16 years
of say the imports of fertilizers which
are given in millions of tonnes okay in
the year 2000 the import was of 1,100
million tons in year 2001 the import was
of 1359 in the year 2002 it was 1015
million tonnes and so on so we have a
data of 16 years we will be plotting
this on a graph graphical sheet and the
plot will be something like this yeah so
here we have you see in the x axis we
have the year the years the first year
that is the 2000 the second year and
that way up to the 15th year this is our
x axis x axis where we have the time
period the time in our case it is the
year okay and here in the y axis
we have the import of fertilizers in
millions of tents fine
so we see in the first year it's 1,100
which is here the second year it is one
thousand three hundred and something and
so on so we have the data and when we
plot these are the values in the
different years and we joined them using
a smooth curve we'll get something like
this okay now this is the actual data
which we have so this is our actual
import fertilizer in the 16 years if you
have to get the trend of this
graphically it's very simple once we
have plotted this graph we simply draw a
straight line through these points and
we assume that this is the most
representative of the line of the curve
so when we draw a straight line through
this this is our trend line okay a line
passing through these points of course
when different people draw this they may
get different lines for example I have
taken this as our trend line maybe
somebody else may come and may you know
take from here something like this you
know somebody else may say that no it's
it's there should be the line which best
fit the value and so on but of course
that that is one of the drawbacks
this is subjective but again it's very
simple and we just have to draw a
straight line through the points okay
so this is our measure of secular trend
looking at its advantages and
disadvantages we see that the merits are
first it is very simple we see that
there is no mathematical calculation
it's simply the plotting the data the
data on a graphical sheet and then
drawing a line through it sex next we
see that it's flexible once once we see
the rigid methods of mathematical trend
and others we'll see that this is very
simple and flexible easily done and
third is that if the observations are
relatively stable the trend can easily
be approximated by this method now this
time is sieves we saw that you know
there was lots of fluctuation but if the
fluctuations are less if the data is you
know relatively stable then we will
easily get a trendline without doing
much without taking any effort okay but
the demerits are that the first it is
subjective and the value of the trend by
different people could be different as
we have seen just now and that it's not
very reliable reason the prediction made
by this method is of little significance
okay because we because of this
objectivity or the subjective nature of
this method okay so that was your
graphical or freehand curve method
method next let's move on to the method
of selected points this is the first
method under the method of averages in
the method of selected points we take
two points and these are considered to
be the most representative of the data
or usually we take the two normal points
and these two are joined by a straight
line to get the secular trend okay so
instead of drawing the line through the
points anyway this time you know we are
fixing up two points any two points and
we join them which two points again
there's subjectivity in that it could be
any two points which we think are the
most representative of the data or which
we feel are normal you know which are
not the extreme points or which doesn't
have much
fluctuations this again is subjective
like the previous one as we have seen
and different person may have different
opinion about the representative points
and further only linear trend can be
determined by this point so let's look
at an example and see how can we do this
and let's take the same you know data we
have the graph you know as we have seen
previously
let's take any two points here let's say
we have taken the first and the last
point so if I take my first and the last
point as my representative and if I join
these two points you know I'll get the
trend something like this this is going
to be my trend line trend line using the
method of selected points okay
now somebody else may come and say that
no these are extreme points let's not
take them let's take knee and say for
example the second point and say the
second last or the last point then of
course our trend value are going to
change it's going to be something like
this
maybe somebody and this can go as viewed
as you know if we take say somebody
feels that these two points are the most
representative or most normal we can
understand how weird the trend value
could go of course my experience the
person knows that you know these are not
the most representative it is one of
these points say one of these points
here or say the points here you know
which are falling in the in between so
again but there's objectivity and it
could lead to you know sometimes error
of large magnitude
so improving upon this let's move on and
next let's take the method of semi
averages the second method in the method
of averages here the given time series
data are divided into two equal parts
and the arithmetic mean of the value of
each part is computed so a little
improvement this time what we do is we
divide the whole set of data into two
equal parts and we take the average or
the arithmetic mean of both these parts
when you do that
each semi average is calculated as
calculated and spared with the center of
the time period - to fit this part and
the two semi averages are joined by a
straight line to get the trend let's see
how it can be done let's take the same
set of data and this time we are doing
with the method of semi averages here
what we will do is we will divide our
set of data into two equal parts we have
totally sixteen data so let's take the
first 8 here 1 2 3 4 5 6 7 & 8 first 8
here and the remaining 8 on the side
let's take the average of both of these
let's go to our excel sheet where we
have our actual data we'll take the
average of these 8 data
and we know that this this will coincide
if we Center it it will coincide with
with mm in between 2003 and 2004 so
let's add them up here this is going to
be you know the sum of or let's stay
okay let's take this sum sum of all of
these 1 2 3 4 5 6 7 & 8
okay and then I need to find the average
average would be this value divided by 8
okay so averages 1 3 7 2 similarly let's
take the average of these 8 say here
okay so we have 1 2 3 4 5 6 7 8
the average of these 8 would be the
value here divided by 8 okay so we have
these two averages here let's plot these
two values 1 3 7 2 and this will
coincide with the middle of these 8 data
let me you know mark these 8 with a
color okay and these it with another
color
fine so we have now this well coincide
with the year between 2003 and 2004 that
is between the fourth and the fifth year
and this will coincide with beer with
the in between 2011 and 12 that is our
12th and 13th year
okay so let's mark them between 4th and
here we will have the first one with
just one 313 72 now we have our 1213 72
will come somewhere over here okay let
me mark this 1372 somewhere over here
and the other data is 1573 1573 will be
between 12 and 13 the data somewhere
here 15 this is our 16 so 15 will be 15
73 will be somewhere here okay now I
have these two data as our semi averages
the semi average one let me call this as
my semi average one and this as our semi
average two if I join these two lines
with a straight with a smooth straight
line I'll get my linear trend linear
trend and this is opposed we will be
joining them with us with a straight
line using scale and pencil so this is
our linear trend of this data
okay so subjectivity has been eliminated
this time but we still have some
problems okay what do we do in case of
odd number of observations well in case
of odd number we still divide the data
into two equal parts by dropping the
middlemost observation let's say we have
say 9 values we will take the first 4
and the last 4 we will leave out the
fifth data ok so that way we get equal
number of data in two equal parts to
obtain the two semi averages which and
these two semi averages are joined by a
straight line to get the trend what are
the advantages and disadvantages of this
the merits the first that again this is
very simple we see that we do not have
you know much of mathematical
calculation as we will be having in the
other methods which will see very
shortly
then it's subjective this time you know
the previous two methods had this
problem that they were subjective this
time it's subjective and anyone applying
this method to a given set of data will
get identical trend value and the D
merits the first is that it only gives
linear trend irrespective of whether it
exists or not
we do not know if the actual trend is
linear or nonlinear irrespective of that
this will only give us a linear trend
second that it's a crude method of
measuring trend since we do not know
whether the effect of other components
is completely eliminated or not so we
still have problem of course these
problems were they even with the
previous ones we assumed that they are
linear and we assume that you know all
the other components are not existing
and so we say that it is a crude method
of measuring and you know these you know
complications we will have to move on
further and use other complex methods
like the moving average and the linear
trend using the the method which we have
seen that is will fit them early in a
trend using the least square method we
shall see these two methods in our
upcoming videos keep watching as UPD of
old videos thank you