Step Deviation Method - Statistics, Mathematics Video Lecture - Class 9

so so far we have stood to method that
is the direct method and the division
met or azumi method now there is one
more method of finding or the mean that
is step deviation method now in the
deviation method what we were doing is
we are actually assuming the one number
that is you are taking it as as as you
mean and we were subtracting that number
number from each of the observations and
after after doing reading actually
reducing our calculation and in the end
for finding out the mean we were
actually adding the same as you mean so
that we are getting the correct mean but
now here in the step deviation method
what we can do is other than finding out
the deviation that is exile minus a what
we are doing here is what we will do
here is we find out the UI also an UI is
actually X I minus a that is deviation
divided by H and H is some random value
that we can take H is some random
variable that we can take and divide
this deviation by s so that it will
reduce the number even further and
accordingly you will get smaller number
and enter makes the calculation much
easier and faster so dead sorry we're
doing here here we are dividing that
nominal deviation by edge so that we can
be able to reduce the number even more
so this is known as the step deviation
method and after doing this what we were
doing is we actually need to find out
the submission of F I you I because in
the biggest case we are actually taking
the deviation debts or rats while you
are doing fi da but now we have further
dividing the deviation by that edge so
accordingly we take fiu I and for
finding out the mean what we need to do
is we definitely have to add the assume
anyone doing in the previous case and
apart from this we also had to multiply
this submission of FI UI / submission of
fi e by h because actually we are
dividing it bad so for finding on the
mean we definitely have to multiply it
by edge and then you need to add
assuming so accordingly we will get the
correct me but this is the method of
finding out the mean by the step
deviation method and this myth is all
this method actually beneficial when we
have the large number or numbers of the
very every other large numbers in the
observation and veteran and to make the
calculation much easier and faster we
had here to reduce those numbers to the
smaller numbers and then we should be
able to do the calculation properly and
and quickly so accordingly we will see
you somewhat an example based on this
and then we'll be able to understand how
to get the mean by the step deviation
method first we write down the example
that is first we die down the
observations and the frequency is given
on the business of dead so let's take
the observations as 808 28 6909 2980 and
let's take 1,000 and let's see the
frequencies at seven fourteen nineteen
twenty five twenty ten and five these
are the observation and frequencies we
have taken now accordingly what we
louvers first we'll take the assume mean
so accordingly the same method molec
first-rate kazumi
morning you will take the edge so let's
take the assumed meanness let's take 900
900 is the middle values among all these
observations so let's take the assume
meanness 900 and take the value of HS
let's take 20 because all the values of
x are actually divisible by all 24 rest
of your ignorance 20 because we also
have to keep in mind this ended after
dividing it by ash we definitely will
not get the decimal value because if we
get a decimal value then our calculation
will get increased but better to take
the integers or integers where you after
dividing it by H so accordingly we need
to take the value of h subject so that
will not get the decimal value so now as
you have taken the assuming an edge and
now what we'll do first first we'll find
out the deviation that is di so as we
find out where Debbie deviation what
will get here is division as we know is
observations minus as you mean so
observation is air as a 800 assume mean
is 900 so that's why I accordingly the
deviation is so accordingly the
deviation really get is x I minus 8 a-10
800-900 minus hundred eight twenty minus
nine hundred minus eighty eight sixty
minus nine hundred minus 40 0 28 t and
hundred this is the value of div God and
now what we ever need to find out we
need to find out UI UI is bi / H so
accordingly minus hundred divided by
twenty will get as minus five minus 80 /
20 minus four minus 40 / 20 minus 20 1
it Wendy / 21 80/20 will get four and
hundred divided by twenty
get five so accordingly this is the
value of you I will EV God because if we
need to find out that if we keep finding
out the mean here by the direct method
then definitely or calculation get
increased because to do the calculus
calculation like a Trinity 27 here then
a turned into 14 it will actually
increase of calculation by very large
extent that's why we have done it like
this that we have receptor taken the
assuming and edge and accordingly we
have reduce the observations because
after subtracting from ajumma also we
were getting the big bad news like
hundred eighty 40 and then x frequency
which again will give us the big bigger
values or greater number so again what
we have done we have again reduced the
deviation to the smaller number by
dividing it by H and now we got at minus
k 5 minus four minus 2014 5 and this is
comparatively the smaller values as
compared to the X or D at or the DI dat
is deviation and now what we do is we
will find out the FI you I that is will
multiply this you are a bit frequencies
so that is 70 x minus 5 so according
will get minus 35 14 x minus 4 so
accordingly will get minus 56 19 x minus
2 we get minus 30 80 20 40 and 25 so
this is the value of fiu IV God and our
frequency is given birth 714 nineteen
twenty five twenty ten and five now what
we do is we add up this fiu I and some
of this fi my will be if you add all
this term accordingly what will get is
40 + 20 60 + 4 80 85 85 minus 35
accordingly at 50 the 50-50 6-6 and
minus six minus 38 will give us the
value minus 40 for the end submission of
fi because we need to divide the
submission of fiu I by submission of fi
37 plus protein 21 verse nineteen forty
forty plus 25 65 plus twenty 85 + 10 95
plus 500 so this is the value of e code
of fi and now if I were finding out the
mean what we need to do is we take the
assume means what you mean we have taken
it as 900 plus h h is 20 * submission of
fiu I'd it is minus forty four divided
by submission of fi hat test hundred and
now this is much easier to solve as
compared to gtf take their it by direct
method or or even this division method
so step deviation method is much more
useful when when we have much larger
number as we have taken then come back
numbers in division method they were
they were comparatively smaller number
as compared to the numbers that here
taken in this particular example so they
are much larger number the texture we
have done it by step division method
because there then the number get
reduced to very smaller number and now
the solid what will get is 20 we will
cancel this fight so now we'll get a 900
minus forty 4/5 and 44 / 5 if you do
what accordingly you will get is
according will get the approximate value
that will be equal to 44 / 5 image of
8.8 and now if we subtract it
what will get nine hundred minus eight
point three so accordingly we'll get
s890 1.2 so this is a mean people and if
you're done it very direct method or
even the deviation method or definitely
we get the same menu but calculation
will become much larger and here you are
saying calculation is has become much
less as compared to the direct method or
they even litigation method and we have
got the answer in just two steps of the
mean and even the table is not even what
we've been complicated and if you are
finding out the submission of fiu I and
solution of fi so even a table is not
much complicated so this is the method
of finding out the mean that we have
studied three method and by using any of
the three method we can actually solve
any frequency distribution table and get
dummy and in the same way as we have
seen here at how to solve that if there
are discrete frequency distribution
table and for finding of the mean in the
same way if you go instead of the
discrete frequency distribution table if
we get continuous frequency distribution
table if we get continuous frequency
distribution table
what we need to do is the container is
requisite distribution table definitely
what we need to do is there are class
intervals and given with the frequencies
and what we can do we actually need to
find out the observations or X let's say
class marks for finding out the mean and
like suppose if I take any example based
on this let's take the class intervals
as you know the continuous frequency
distribution table consists of class
intervals and frequencies so let's stay
in the class interval has 0 to 20 20 to
40 40 to 60 then 60 to 80 and
accordingly 80 to 100 and accordingly we
take the frequencies as 15 8 21 29 and
17 so accordingly these frequencies we
have taken no definitely at the class
intervals are together we could not be
able to find out the mean directly
because for finding out the mean we
definitely mean need the observation so
what we can do here will actually find
out the class marks that is X and glass
mask we have already know about to find
out that is up upper limit plus lower
limit divided by 2 this is the method of
finding out the class was that we had
studied in class 9th that is so
according in the class much will get a
zero past 20 / to get is 1030 50 70 and
90 so this is the class must be God and
now as we got the class mass that x and
frequencies now by using any of the
methods like direct method stab division
method or
method we can easily find out the mean
so if you need to find out the meaner
like like we can also use the deviation
method here or disturb division method
here also that's not an issue so if we
take a like if it do it by step division
method definitely we need to take the
assume mean and let's take the assume
mean as 50 because it is the middle
value among the glass mask and let's
take hs10 so now according you will find
out the deviation end deviation and you
I so accordingly divisional is 10-50
that is minus forty minus 20 0 20 and 40
this is a deviation record and you I
because again it's a little bigger value
so that's why we have taken hs10 or you
can also take hs20 so if you take HS 10
or 20 it will reduce the value let's
take HS 20 min so accordingly because
all these are the multiples of 20 40 20
all these are the multicolored me so
that's why we can take 20 also so
accordingly UI is di / H that is minus 2
minus 1 0 1 and 2 and now accordingly
what we do is we find out the value of
so accordingly we find out the value of
F I you I and fri is frequency into you
I dated 15 into minus 2 is minus 38 into
minus 1 is minus 80 20 19 21 29 and 17
in to do is 34 and if you take the
addition of this again we'll get the
much smaller values for 34 + 39 if we
add will get 63 and 63 minus 30 3333
minus 8 so we'll get 25 so for finding
out the mean what we need to do assume
mean that is 50 plus h that is 20 into
submission of fiu is 25 / submission of
fi dat is summation of frequency so if
you had this frequency what we get is 15
plus 8 23 + 31 44 44 plus 2973 plus 17
so accordingly we will get 90 here now
if you solve it 00 will get cancelled so
you get 50 plus 50 by nine and if you
solve it what will you get 50 plus 50 x
9 30 by nine is approximately five point
five five so accordingly let the meanest
55.5 5 this is the method of finding out
the name by using any by using any of
the method line staff division division
of direct method and this is this way
and find out the mean in case of
continuous frequency distribution table
so again same method but here you
definitely need to take the class maths
because class intervals should be given
in if the cuddles frequency distribution
table is given definitely you need to
take the class marks and accordingly by
using any of the methods you can find
out the me