Class 10 Exam > Class 10 Videos > Crash Course: Class 10 > Median of Grouped Data
Median of Grouped Data Statistics - Maths Class 10
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210 videos
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FAQs on Median of Grouped Data Statistics - Maths Class 10
| 1. What is the concept of median in grouped data? |  |
Ans. The concept of median in grouped data refers to finding the value that divides the data into two equal halves. In grouped data, the median is the value that lies in the middle of the data when arranged in ascending or descending order. It is often used to represent the central tendency of the data.
| 2. How is the median calculated for grouped data? | |
Ans. To calculate the median for grouped data, the following steps can be followed:
1. Determine the cumulative frequency of each class interval.
2. Find the class interval that contains the median value.
3. Use the formula: Median = L + ((N/2 - CF) * h)/f
- L: Lower limit of the median class
- N: Total frequency
- CF: Cumulative frequency of the class before the median class
- h: Class width
- f: Frequency of the median class
| 3. How is the median affected by outliers in grouped data? | |
Ans. Outliers in grouped data can significantly affect the median. If there are extreme values present in the data, they can pull the median towards them, resulting in a distorted representation of the central tendency. It is important to identify and handle outliers appropriately to ensure the accuracy of the median.
| 4. Can the median be calculated for qualitative data in grouped form? | |
Ans. Yes, the median can be calculated for qualitative data in grouped form. In this case, the classes represent different categories rather than numerical values. The median is determined by finding the class interval that contains the middle value and applying the formula mentioned earlier using the respective frequencies.
| 5. What is the significance of the median in analyzing grouped data? | |
Ans. The median is significant in analyzing grouped data as it provides a measure of central tendency that is less affected by extreme values or outliers compared to the mean. It gives a better representation of the typical value in the data set. The median is commonly used in various fields such as statistics, economics, and social sciences to understand and interpret data accurately.
Text Transcript from Video
hello friends this video at the six part
10 is brought you by exam fear calm no
more fear from exam before watching this
video please make sure that you have
watched part 1 to part 9 till now we
have studied in need and more Oh group
rhythm correct yes with all this 3 so on
Mina we have 3 methods direct method
step division method and the zooming
method and for more we have only one
method and all this way for good beta
normal study median of group Rita
actually but before we start the median
of group data let me solve a question
using media love unglue beta so as you
will get the understanding of how to
find million of unglue beta and then
we'll proceed with made you know Rho
beta to start with let me recap lit what
I have told are real median is nothing
but a measure of central tendency which
gives the middle most value correct it
will give the middle most value in the
given it does it for example in this
case we have number of students must
obtain by students twenty by six
students 29 by 28 like this we have the
data and for this we have to find median
so to find million the first thing we do
is we arrange our aligned ascending
order the smallest is 20 so we'll write
20 percent
then comes 25 so all right 25 next then
comes 28 I suppose young sis 28 then is
29 and then we have 33 then I have 38
and then I have 42 and then I have 43
that is the first thing I did I wrote
data in ascending order and let me I'd
corresponding frequency 420 that it fell
says 6 so this guy is 6 for 25 the
frequency is 20
24:28 the frequencies 24 so this noise
to any form for 29 the frequency is 28
for 33 the frequency is 15 for 38 the
frequency is for 42 the frequency is 2
and 43 the frequencies so I wrote the
frequency the first thing is in the
ascending order and then this is the
frequency the second thing is I have to
write that come with little equation
cumulative frequency is something we add
this frequency for previously conceived
there is no previous Lewin see if this
becomes 6 in this case it is 20 plus 6
this becomes 26 in this case is 26 plus
24 that becomes 50 here it is 50 plus 28
that is 78 here it is 78 plus 15 that is
93 here it is 93 plus 4 97 97 plus 2 99
and then plus 1 that is 1 so this is how
I wrote the cumulative fitness second
thing is the number of observation is
hundred correct since of number of
observations hundred I have to take n by
2 and N by 2 8 plus 1 right n by 2 s
plus 1 observation and my do is what 50
that is 58 and n by 2 plus 1 is 50 f51
observation I have to take these values
what is the value of 50 the observation
so you see 15 till 50 it is in this
range so 15 all the way here is Wendy
wait so this guy's 28 50 second or 50
first will now lie in this bracket
because 51 to 78 is in this bracket so
50 first is 29 this valence should and
take the mean of this therefore
median will be nothing but mean um 28
and 29
thus becomes 28 point and that is how we
find the median to find median the first
thing is we arrange the value at the
sending order we find a cumulative
frequency then if the number is odd
sorry even then we take n by 2n n by 2 +
1 observation the number is odd we take
n plus 1 by 2 wave observation only
correct in case it is odd this thing we
have learned in the other classes in
case it is even we take n by 2 and n by
2 s plus 1 elevation we found those
values this value we found and then we
take the mean if it is odd number then
we take n by n plus 1 by 2 of the B for
example 1 2 3 3 numbers what does I have
to find median the number of observation
is odd that is 3 so I take 3 plus 1 by 2
to it that is second mother second value
is 2 this is will be why median in case
the value is something I did 1 2 3 4 and
here you see n is even so I'll take n
may do an N by 2 plus 1 that is 4 by 2
and 4 by 2 plus 1 that is 2nd end heart
down second number is 2 and third term
is 3 I'll take this value find the mean
that is 2 plus 3 by 2 that is 2 point 5
and this will become a medium please
think we have done in the other classes
just I want to revise things if the
understanding for median of ungroup'
data is clear we can proceed with the
median of Rue Breda he have the same the
definition let's repeat median is
nothing but central tendency which gives
the middle most value of the awesome
here the formula we are using is median
is L plus M by 2 minus C F by F into H
I'll explain what this terms are L is
the lower limit of the middling class n
is the number of observations CF is the
cumulative frequency of the class
preceding the middling class and F is
the frequency of
class and H is the class size these are
the values I will do I will solve in
question to explain this this understand
learn this formula the formula says
medians n plus n by 2 minus EF by F into
H where L is the lower limit of the
middle class and there is the number of
observations CN is a cumulative
frequency class preceding the median
class F is the frequency of muting class
and s is the de l'espace building my
example the question says the following
trick when Z distribution gives the
monthly consumption of electricity of 68
consumers of a locality we have to find
the median so if you see this it is a
group leader why it if identify one not
five about five you see this value of
125 125 that means it is a group data
also if you want to find the class
length 85 minus 65 21 not 5 minus 85 21
25 minus 1 1 5 21:45 - 125 21 65 ml 1 /
2 8 24 8 2 5 minus 165 22.5 - 1 5 20 so
20 is the plus that means it is a good
data first thing is clear now I can use
the funda
it is already arranged in ascending
order the first thing is to align in
ascending order it is already arranged
in the ascending order
so let me write in this fashion the same
thing I wrote in this fashion doesn't
ascending order and it is a pregnancy
the first thing we should do is we have
to find cumulative frequency in case of
medium so let us do this here - before
here d 4 + 5 9 9 + 13 22 22 + 20 42 42 +
14 30 56 56 + 8 64 + 64 + 4 is 16 so I
found of cumulative signals now if you
see the number of the vision is 16
because the maximum value of community
is a number of observation so n comes
out to be 16 and n here in this case is
even number correct so in this case my
cumulative frequency will be I mean the
media class will be the place where n by
2 and n by 2 plus 1 value lies n by 2 is
how much 68 by 2 that is 234 and 34 n by
2 plus 1 is 35 so 34th and 35th if you
see both line in this one this class
right because this has been strong 23 to
40 so this is my median in class the
first problem is solved we have the
middle class correct because this is the
leading class why because the median
class should have the value 34th and
35th term should be in the median class
and we found that this is a median
logical 34th and 35th um this is this
class now the formula is we know very
simple the formula is median is nothing
were helpless n by 2 minus C F by F into
H what is the value of L L is the lower
limit of the meeting law that is 125
this is the value of L let me put the
values here L is equal to 125 what is
the value of n by 2 sorry m and a 68 we
do this I will open and it's 68
correct what is CF CF is nothing word
humility frequency of the class
preceding media class this is the
meeting last so community frequency of
this class is called CF so CF turns out
to be
- I have CF what is F F is nothing but
the frequency of the median class this
is the frequency of the meaningless
please note I am NOT taking the
cumulative frequency of reading class
I am taking the frequency of the median
class what is the value of H that is
nothing but class interval so you see
the class interval is 20 here it is
please understand the main thing is
understanding these values l came out to
be 125 because L is nothing but lower
limit of media class 125 n is 68 the
number of items CF has a cumulative
frequency of class listening media class
22 frequency is the frequency of the
meeting class and s is a closet we put
the values here this becomes 125 plus 68
n by 2 minus CF is 22 by F F is 20 into
H in illustrator
Jensen this becomes 125 plus this
becomes 34 34 minus 22 is 12 this joy
this comes out to be 140 so the monthly
consumption of electricity is 137 units
and this is the medium thank you visit
exam viacom to watch free education
videos try 3 on my test in the best
quality study materials study from the
best tutors and mentors and much more
thanks Anne screen
10 is brought you by exam fear calm no
more fear from exam before watching this
video please make sure that you have
watched part 1 to part 9 till now we
have studied in need and more Oh group
rhythm correct yes with all this 3 so on
Mina we have 3 methods direct method
step division method and the zooming
method and for more we have only one
method and all this way for good beta
normal study median of group Rita
actually but before we start the median
of group data let me solve a question
using media love unglue beta so as you
will get the understanding of how to
find million of unglue beta and then
we'll proceed with made you know Rho
beta to start with let me recap lit what
I have told are real median is nothing
but a measure of central tendency which
gives the middle most value correct it
will give the middle most value in the
given it does it for example in this
case we have number of students must
obtain by students twenty by six
students 29 by 28 like this we have the
data and for this we have to find median
so to find million the first thing we do
is we arrange our aligned ascending
order the smallest is 20 so we'll write
20 percent
then comes 25 so all right 25 next then
comes 28 I suppose young sis 28 then is
29 and then we have 33 then I have 38
and then I have 42 and then I have 43
that is the first thing I did I wrote
data in ascending order and let me I'd
corresponding frequency 420 that it fell
says 6 so this guy is 6 for 25 the
frequency is 20
24:28 the frequencies 24 so this noise
to any form for 29 the frequency is 28
for 33 the frequency is 15 for 38 the
frequency is for 42 the frequency is 2
and 43 the frequencies so I wrote the
frequency the first thing is in the
ascending order and then this is the
frequency the second thing is I have to
write that come with little equation
cumulative frequency is something we add
this frequency for previously conceived
there is no previous Lewin see if this
becomes 6 in this case it is 20 plus 6
this becomes 26 in this case is 26 plus
24 that becomes 50 here it is 50 plus 28
that is 78 here it is 78 plus 15 that is
93 here it is 93 plus 4 97 97 plus 2 99
and then plus 1 that is 1 so this is how
I wrote the cumulative fitness second
thing is the number of observation is
hundred correct since of number of
observations hundred I have to take n by
2 and N by 2 8 plus 1 right n by 2 s
plus 1 observation and my do is what 50
that is 58 and n by 2 plus 1 is 50 f51
observation I have to take these values
what is the value of 50 the observation
so you see 15 till 50 it is in this
range so 15 all the way here is Wendy
wait so this guy's 28 50 second or 50
first will now lie in this bracket
because 51 to 78 is in this bracket so
50 first is 29 this valence should and
take the mean of this therefore
median will be nothing but mean um 28
and 29
thus becomes 28 point and that is how we
find the median to find median the first
thing is we arrange the value at the
sending order we find a cumulative
frequency then if the number is odd
sorry even then we take n by 2n n by 2 +
1 observation the number is odd we take
n plus 1 by 2 wave observation only
correct in case it is odd this thing we
have learned in the other classes in
case it is even we take n by 2 and n by
2 s plus 1 elevation we found those
values this value we found and then we
take the mean if it is odd number then
we take n by n plus 1 by 2 of the B for
example 1 2 3 3 numbers what does I have
to find median the number of observation
is odd that is 3 so I take 3 plus 1 by 2
to it that is second mother second value
is 2 this is will be why median in case
the value is something I did 1 2 3 4 and
here you see n is even so I'll take n
may do an N by 2 plus 1 that is 4 by 2
and 4 by 2 plus 1 that is 2nd end heart
down second number is 2 and third term
is 3 I'll take this value find the mean
that is 2 plus 3 by 2 that is 2 point 5
and this will become a medium please
think we have done in the other classes
just I want to revise things if the
understanding for median of ungroup'
data is clear we can proceed with the
median of Rue Breda he have the same the
definition let's repeat median is
nothing but central tendency which gives
the middle most value of the awesome
here the formula we are using is median
is L plus M by 2 minus C F by F into H
I'll explain what this terms are L is
the lower limit of the middling class n
is the number of observations CF is the
cumulative frequency of the class
preceding the middling class and F is
the frequency of
class and H is the class size these are
the values I will do I will solve in
question to explain this this understand
learn this formula the formula says
medians n plus n by 2 minus EF by F into
H where L is the lower limit of the
middle class and there is the number of
observations CN is a cumulative
frequency class preceding the median
class F is the frequency of muting class
and s is the de l'espace building my
example the question says the following
trick when Z distribution gives the
monthly consumption of electricity of 68
consumers of a locality we have to find
the median so if you see this it is a
group leader why it if identify one not
five about five you see this value of
125 125 that means it is a group data
also if you want to find the class
length 85 minus 65 21 not 5 minus 85 21
25 minus 1 1 5 21:45 - 125 21 65 ml 1 /
2 8 24 8 2 5 minus 165 22.5 - 1 5 20 so
20 is the plus that means it is a good
data first thing is clear now I can use
the funda
it is already arranged in ascending
order the first thing is to align in
ascending order it is already arranged
in the ascending order
so let me write in this fashion the same
thing I wrote in this fashion doesn't
ascending order and it is a pregnancy
the first thing we should do is we have
to find cumulative frequency in case of
medium so let us do this here - before
here d 4 + 5 9 9 + 13 22 22 + 20 42 42 +
14 30 56 56 + 8 64 + 64 + 4 is 16 so I
found of cumulative signals now if you
see the number of the vision is 16
because the maximum value of community
is a number of observation so n comes
out to be 16 and n here in this case is
even number correct so in this case my
cumulative frequency will be I mean the
media class will be the place where n by
2 and n by 2 plus 1 value lies n by 2 is
how much 68 by 2 that is 234 and 34 n by
2 plus 1 is 35 so 34th and 35th if you
see both line in this one this class
right because this has been strong 23 to
40 so this is my median in class the
first problem is solved we have the
middle class correct because this is the
leading class why because the median
class should have the value 34th and
35th term should be in the median class
and we found that this is a median
logical 34th and 35th um this is this
class now the formula is we know very
simple the formula is median is nothing
were helpless n by 2 minus C F by F into
H what is the value of L L is the lower
limit of the meeting law that is 125
this is the value of L let me put the
values here L is equal to 125 what is
the value of n by 2 sorry m and a 68 we
do this I will open and it's 68
correct what is CF CF is nothing word
humility frequency of the class
preceding media class this is the
meeting last so community frequency of
this class is called CF so CF turns out
to be
- I have CF what is F F is nothing but
the frequency of the median class this
is the frequency of the meaningless
please note I am NOT taking the
cumulative frequency of reading class
I am taking the frequency of the median
class what is the value of H that is
nothing but class interval so you see
the class interval is 20 here it is
please understand the main thing is
understanding these values l came out to
be 125 because L is nothing but lower
limit of media class 125 n is 68 the
number of items CF has a cumulative
frequency of class listening media class
22 frequency is the frequency of the
meeting class and s is a closet we put
the values here this becomes 125 plus 68
n by 2 minus CF is 22 by F F is 20 into
H in illustrator
Jensen this becomes 125 plus this
becomes 34 34 minus 22 is 12 this joy
this comes out to be 140 so the monthly
consumption of electricity is 137 units
and this is the medium thank you visit
exam viacom to watch free education
videos try 3 on my test in the best
quality study materials study from the
best tutors and mentors and much more
thanks Anne screen
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Nov 23, 2024 Last updated |
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