Mean Deviation for grouped Data About Mean Video Lecture | Mathematics for GRE Paper II

hi friends in this session we will see
the numerical based on mean deviation
through mean of group date
here you see find the mean deviation
from mean of the for the following data
the class interval is given here 0 to 10
10 to 20 20 to 30 30 to 40 40 to 50 is
given and the frequency is given here 5
8 15 16 6 these have been given so we
have to find out the mean deviation you
see here the formula for mean deviation
here you see Delta X bar is the mean
deviation through mean is equal to
summation of F mod of X minus X bar over
summation of if this would be the
formula so for this we have to find out
first of all X minus X bar the in this
formula you can see X bar is compulsory
to find out so first of all we would
find out the X bar for X bar we need the
mid value of this class interval which
we will get through I explained you here
0 plus 10 divided by 2 is equal to 5
here you see then we could get the mean
mid value through this way or I will
explain you some other way also so it
would be 30 by 2 is 15 so you see the
class difference is class width is same
in all the class intervals so the class
width is 10 10 minus 0 10 so we have
first we have find out the first mid
value then add 10 to each mid value we
will get the succeeding mid values so
here we will get 25 here we will get 35
here we get four define these are the
mid values now what we have to do we
have to find out I've into X FX so 5
into 5 25 15 into 8 130 so I won 20 25
into 15
375 35 into 16
five sixteen forty five into six
270 ok so this we have what here now
what we have to do we have to first find
out the X bar just I calculate this need
1,300
50 this we have got here now summation
off we will get here 5 8 13 or 15 28 28
and 644 650 so it is 15 okay so first we
find out this mean because X bar is
equal to summation of FX over summation
of f this is the formula for mean in
discrete data so X bar summation of FX
we have here 1 3 5 0 and summation of f
is 50 so we will get
27 so we got 27 as mean for this data
27 it is the x-bar so what we have to do
X minus X bar X is here we have to
subtract 27 from these so 5 minus 27
why - 27 - 22 15
- 27 - 2 n 25 - 27 - 235 - 27
eight
45 - 27 Eddie
so you have got this now we will make
the
we'll make the absolute value of this
all we will get their salute value so it
is 22 no it is 12
it is 2 it is 8 deserting so now what we
have to do we have to multiply this with
F F into mod of the X deviation from
mean so we have to multiply these two
you so we will get 110 here 12 6 15 2
times 30 16 8 times 128 + 18 6 times 180
so we have got this and now we will make
the summation of this all 110 plus 96
plus 30 plus 128 plus 1 0 8 relate 472
for 472 here so in this formula we have
to put this summation of F into absolute
of DX bar and over summation of F so in
this formula we put this Delta X bar
is equal to summation of in this formula
we are putting the value for 72 over 50
so we get here nine point four four nine
point four four so this would be the
mean deviation for this sort of data and
this is the group data very easy to
solve what we have to do we have to
first of all in group data find out the
mid value then multiply the mid value
with frequency effects summation of FX
and summation of f we get through this
to mean if we get the mean we get the
deviation from mean of whole the mid
values five minus twenty seven and
fifteen minus twenty-seven the mean
whatever we have what we deviate and we
get the deviation from mean of all the
data when we get the deviation from mean
we make its absolute value we make all
positive here and then we multiply these
values absolute deviation with frequency
so we get the this frequency and
absolute values product and they we
submit a summation of this all we put in
this formula and summation of a F we
again put in the denominator of this
formula we get be in Daviess