Example of Mean Deviation about Median for Discrete Frequency Distribution Video Lecture | Mathematics for GRE Paper II

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for example where we had to find the
mean deviation about median or the swell
so the first step we have to do is we
have to arrange in ascending order if
you see to verify B is more ascending
order so let's tie in this first
ascending order
alright so let me write this this xi5 so
the minimum is 2 so like okay then comes
five nine five eight then comes six
alright since ten then comes eight
answer then comes 10 alright then it and
that comes together so like 12 I so now
I have this in ascending order
the second step is to find the value of
N and here it is off to find a
cumulative frequency to find it
accumulated message that will give the
value of n altogether so this becomes
the cumulative frequency at this point
will be 2 it will be 2 plus 8n it will
be 10 plus 10 is 20 20 plus 7 27 27 plus
a 35 and this is 40 that means is a
total number of terms and is going 40 if
you can directly record because the last
value is the total number of terms now
to find me again what we have moved
since n is equal to 40 so the median
term is nothing but n by dou Y by 2 plus
1 because this is even so that means ten
and eleven term we are looking
now from this distribution we can say
that ten come in this movie and eleven
doesn't this box I think I made a
mistake here I think I made a mistake
here and it's birthday party so this is
n by 2 is 20 and N by 2 plus 1 is 21 so
I'm looking for 20th and 21st term the
creative a clearly 20th and 21st are
looking for these two terms so 20th job
will be in this in this box and 20th
will be the this so I have to take the
mean of 6 and 2 why because I am doing
for 20th and 21st term this is still
28th so 20th will be in this bar 24th on
verse is in this box
that means 21 22 23 everything is in
this box
so 20th dumbest say 28 term is 6 and
21st terminus
so the median in my case will be the
median will be nothing worth 6 plus 8
divided by 2 that is correct so we have
got a median first thing achieve good we
have media not now we have been in then
we can now find mean deviation above
would media to final mean the vision
about median what we have to do we had
find the census of all these points
about begin
so after I write x i- m so distance of 2
from 7 is that equal to a minus 7 or
that comes out to be fine do this very
intimate similarity distance of 5 from 7
is nothing but pi u -7 mod that is
nothing but d is furthest distance of 6
from 7 as the think word 6-7 more that
is nothing but 1
as well similarly distance of 8 from 7
is nothing but 8 - 7 more and that is
also 1 similarly this is of them from 7
is nothing but 10 - 7 more distance of
10 from 7 is nothing but 10 - 7 more
that this 3 this guy is 3 and distance
of 12 from CERN is nothing but 12 minus
7 that is see everything if you write in
the tabular form it is very easy to
calculate it's not conclusive also so
now I have found exciting - but a
formula which I had was was of something
of this form
I like the formula the formula was of
this form Sigma fi into X minus M right
by Sigma there was a palm block mean
deviation about medium correct so we
have to find Sigma fi X I so first we
define a fight this one Sigma fi XA
minus M so that's fine FY into X I minus
M 1
it's okay to multiply these together
make it circle if you want to multiply
these two so what we'll get is nothing
but FY into exile - and this is more -
this is nothing but 5 into 2 is 10 8
into 2 is 16 6 10 into 1 is nothing but
10 7 into 1 is nothing but seven eighty
degrees nothing but 24 5 into pies
anyone
this becomes totally if your and this
becomes 25 plus $24.99 49 49 plus 7 is
56 66 70 we need to make do
yes 90 do so according to formula
MD is nothing but seen from there right
see Wi-Fi into exile - bye
si Maya fine where I is equal to 1 to 12
Heroes Y is equal to what - this is all
I this becomes this is 90 to be found
this value I need to buy see my FIV know
else nothing but 40 right if you add
this because party my father so this is
so the mean deviation about median for
this detail 92 by 40 what we have done
the first thing is we found the mean to
fight the way we arrange this in
ascending order all the exercise first
year this is wrenching on it we found
the cumulative frequency it came out to
be CF came out to be 40 since it is an
event number to find the mean we have to
get n by 2 with n by 2 plus 1 that we
have learned in the past classes so we
have to find 20th and 21st oh we found
20th some is 60 and 21st n is a we took
the me mean of this to get the medians
median came out to be user once we got
the median now we have found a distance
of excise from median the this is him of
to be used fellows fight to one man will
be fine once we have a distance we found
a file into the distance record distance
we added this to get 92 and then we use
the formula the formula was Sigma of fi
into x i-
it's distance by Sigma FY where I tends
to ayiva
that is from one to play we put the
values and we got the answer is nine to
one thank you
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