Examples Mean, median and mode Video Lecture - Class 6

hello friends this video on data
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let us try to calculate medium for even
number of observations so let's say that
the scores and mathematics test of 10
students is as follows so this is a data
for 10 students and we have to find out
the median so the first step would still
remain the same
we just need to arrange it in ascending
order so once you are injured in
ascending order you get something like
this five nine ten fifteen sixteen
nineteen twenty twenty three twenty five
so twenty is repeated twice so twenty
twenty twenty three twenty five so this
is your data arranged in ascending order
now will you be able to find out a
middle most number here you can't
because you know there there is no such
number which will be the middle most so
if you consider sixteen so this side you
have four but this side you have five so
16 is not the middle most number if you
consider nineteen this side it is four
but this side it is five so nineteen is
also not the middle most number but
basically the middle most number should
lie somewhere in between these two right
because this side also you have five
this side also you have fine so this is
somewhere the middle most number should
lie so how will you calculate the middle
most number no matter the most number is
nothing but the median so median or the
middle most number would be the average
of 16 and 19 because we believe that the
middle most number is somewhere in
between these two so how will you
calculate it some of these two sixteen
plus 19 divided by 2 2 because we are
dealing with two numbers so 16 plus 19
is 35 divided by 2 which is equal to
seventeen point five so seventeen point
five will be the median of this set of
data so whenever you talk about odd
more observations the value of median is
one of the existing data from that set
of data but when you talk about even
number of observations like this man the
value of median is not seen in this data
it is something else outside this data
for example 17.5 is the median in this
case but 17.5 is not one of the existing
data out of this set of data right so
therefore only for odd number of
observations the value of median is
actually one of the data in the group of
data so let us now quickly look at some
of the questions based on mean median
and mode question number one the ranch
code in a cricket match by 11 players is
as follows
find the mean median and mode of this
data are the three same so first of all
what we do is we arrange the data in
ascending order so we arranged it in
ascending order so what do we get we get
something like this 6 8 10 10 15 15 15
50 80 100 and 120 so this is what we get
so total so select let us also try to
arrange the same data in tabular form so
how do we arrange it in tabular form so
we have one column for the runs and we
have another column for the frequency if
you want you can have another column for
tally as well otherwise you can directly
have frequency also so that here what we
will do is in this table we are not
going to repeat the data instead we are
just not going to write everything just
once but we will write their frequency
how many times 6 is getting repeated 1 8
1 10 2 times 15 3 times 50 again 180
again 100 is also 1 and 120 is also 1 so
this is how we have established
the frequency distribution table so we
have arranged the data in ascending
order as well as in tabular form now we
can very easily calculate all the values
so first week actually to mean so mean
is nothing but some of the values that
is sum of all these values divided by
how many values do you have definitely
you have eleven values because these are
the runs scored by eleven players so you
would find it out like this six plus
eight plus 10 plus 10 plus 15 plus 15
plus 15 plus 15 plus so on till 120
divided by 11 so the sum comes out to be
420 9/11 this is equal to 39 so the
average or the mean of these data is 39
next we have to find out mode so mode
represents that data with maximum
frequency so let's look at the frequency
distribution table this is the maximum
frequency which data for response to
maximum frequency it is 15 therefore
hold will be 15 next we have to find out
the median median is the middle most
data so here when it has been arranged
in ascending order
we have total 11 pairs so we can divide
it into groups of five five so one two
three four five this five in one group
and again from the end one two three
four five this five in the other group
so which is the middle moves today time
so the middle most data is 15 so what do
we observe we observe that in this case
more than median are the same but they
are not the same as mean therefore no
all the three are not same question
number two find the mode and median of
the data 13 16 12 14 1912 14 13 and 14
so first of all we need to arrange it in
ascending order so we get 12 12 13
14 14 14 16 and 19 so this is how we
have arranged it in the ascending order
we can also make its frequency
distribution people so let's say we have
one column for the data and the other
column for the frequency so what are the
numbers that we have 12 13 14 16 and 19
so if we look at their frequency 12 is
repeated twice 13 is also repeated twice
14 is repeated thrice 16 ones and 19 is
also ones so in this case what would be
the mode so mode corresponds to the
number with maximum frequency so maximum
frequency is 3 and the number
corresponding to maximum frequency is 14
and what would be the median so median
is the middle most term so here 1 2 3 4
5 6 7 8 9 so we can divide it into 4
groups of 4 and 4 so the middle most
number in is 14 so in this case we see
that the mean anthem that the median and
the mode of this set of data are the
same tell whether the statement is true
or false more is always one of the
numbers in a data so do you think mode
is always one of the numbers in a data
mode is a number in that set of data
which has maximum frequency so
definitely it has to be one of the
numbers in that data mean can be one of
the numbers in a data will mean so mean
yes it can be because here it says it is
not necessary that mean is always one of
the numbers but yeah in some cases it
might be so let me give you an example
so in this case let's take the example
of mean of first five whole numbers you
remember we calculated this some time
back so what are the first five whole
numbers 0 1 2 3 & 4 so when you
calculate their mean what do you get
plus one plus two plus three plus four
divided by five because you are dealing
with five numbers so this comes out to
be 10 by 5 which is equal to 2 so in
this case mean which is 2 is also one of
the numbers in the data so therefore it
is possible that sometimes mean can be
one of the numbers in the data but it is
not necessary that mean will always be
one of the numbers in the data
the median is always one of the numbers
in a data well this is false that is
because median is one of the numbers in
a data only then so this statement is
true only when the total number of data
is odd only when we handle odd number of
data because you remember whenever we
have odd number of data in that case
let's say you have 999 so 4 on this side
and 4 on this side so the median is the
data which is at the middle but when you
have 8 number of data in that case your
median doesn't is not one of the numbers
in the data so you actually take out the
average of the two middle terms and then
calculate the median so in ease of even
number of data median is not one of the
numbers in the data a data always has a
mode well this is not really true
because you cannot see always because
many a times it might happen that the
set of data exists where all of them
have the same frequency so there you
really do not have the concept of a
particular data with maximum frequency
so therefore you cannot see that a data
always has a mode the data 6 4 3 8 9 12
13 9 as mean 9 so for this we will
actually have to calculate the mean of
this data this would be 6 plus 4 plus 3
plus 8 plus 9 plus 12 plus 13 plus 9
divided by 9
and when you actually calculated the
mean comes out to be 8 so the mean is
not 9 the mean is 8 so this is false
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