hi how to get the median if given a set of numbers in ascending order from 5, 6,7,8... to 20000?
i read somewhere the formula for median is as follows:
if n is no of terms,
(1) if n is odd, median is the (n+1)/2 term
(2) if n is even, median= average of 2 middle terms
how to apply
firstly, what are the numbers in the set of numbers that you mentioned?
for square, are the diagonals equal in length and angle?
Originally posted by Divanhot:hi how to get the median if given a set of numbers in ascending order from 5, 6,7,8... to 20000?
i read somewhere the formula for median is as follows:
if n is no of terms,
(1) if n is odd, median is the (n+1)/2 term
(2) if n is even, median= average of 2 middle terms
how to apply
Number of terms = 20000 - 5 +1 = 19996 terms
Medium = (19996+1)/2 = 9998.5 = (9998th + 9999th)/2
9998th term = 5 +9997 = 10002
9999th term = 5+ 9998 = 10003
Medium = (10002+10003)/2 = 10002.5
Originally posted by Divanhot:for square, are the diagonals equal in length and angle?
Yes.
Originally posted by Divanhot:hi how to get the median if given a set of numbers in ascending order from 5, 6,7,8... to 20000?
i read somewhere the formula for median is as follows:
if n is no of terms,
(1) if n is odd, median is the (n+1)/2 term
(2) if n is even, median= average of 2 middle terms
how to apply
You just add the 1st no. and the last no. and then divide them by 2, given that each of the no. is 1 more than the previous no., no more, no less.
In this case, the median will be ( 5 + 20000 ) / 2 = 20005 / 2 = 10002.5
Originally posted by Mikethm:Number of terms = 20000 - 5 +1 = 19996 terms
Medium = (19996+1)/2 = 9998.5 = (9998th + 9999th)/2
9998th term = 5 +9997 = 10002
9999th term = 5+ 9998 = 10003
Medium = (10002+10003)/2 = 10002.5
hi bro mike, for median u use (n+1)/2 where n is the no of terms right?
There are 19996 terms in total, meaning the no of terms are even . so means to get median for both odd and even terms, we can use (n+1)/2 where n is the total no of terms?
thanks
how about a set of nos from 6 to 4999, and the numbers from 6 to 4000 is even( i.e. 6,8,10,12,14.... to 4000) and the numbers from 4001 to 4999 is odd( i.e. 4001,4003,4005,...4999)
how to find the median then?
Originally posted by Divanhot:how about a set of nos from 6 to 4999, and the numbers from 6 to 4000 is even( i.e. 6,8,10,12,14.... to 4000) and the numbers from 4001 to 4999 is odd( i.e. 4001,4003,4005,...4999)
how to find the median then?
This will be slightly more complicated.
The 1st step is to find the amount of numbers in all.
From 6 to 4000, there are (( 4000 - 6 )/2 + 1 ) numbers, which is 1998 numbers.
From 4001 to 4999, there are ((4999-4001)/2 + 1 ) numbers, which is 499 numbers.
Hence, the median will be the (( 1998+499 )/ 2)th number, which is the 1248.5th number, or rather, the result of ( 1248th number + 1249th number ) / 2
The 1248th number will be ( 6 + (1247 X 2)), which is 2494.
Hence, the 1249th number will be 2496, and the median will be 2495.
hi thanks for the clarification bros. one challenging problem is
for a set of nos 9,18,26,31,49,53,59,61, 61.5, 70, 90,
how to find the total number of terms besides counting? any formula?
the number is not in +1 order or +2 order, but random
hi bro forbidden, from no 4001 to 4009, total no of numbers= 500 right
median term= (1998+ 500)/2 = 1249th term, between 1248th term and 1250th term
1248th term= 6 + (1247*2)= 2500
1250th term= 6 + (1249*2)= 2504
median= (2500 + 2504)/2 = 2502
do clarify thxs
Originally posted by Divanhot:hi thanks for the clarification bros. one challenging problem is
for a set of nos 9,18,26,31,49,53,59,61, 61.5, 70, 90,
how to find the total number of terms besides counting? any formula?
the number is not in +1 order or +2 order, but random
Just count. Random numbers as you say can't have a formula
Originally posted by Divanhot:hi bro mike, for median u use (n+1)/2 where n is the no of terms right?
There are 19996 terms in total, meaning the no of terms are even . so means to get median for both odd and even terms, we can use (n+1)/2 where n is the total no of terms?
thanks
Yes, (last term - first term) + 1 always give you the number of terms. You will use this fact more often at A levels in AP GP.
And medium is always (n+1)/2 where n is the number of terms. You do not change just because it is even or odd number of terms.
Originally posted by Divanhot:hi bro forbidden, from no 4001 to 4009, total no of numbers= 500 right
median term= (1998+ 500)/2 = 1249th term, between 1248th term and 1250th term
1248th term= 6 + (1247*2)= 2500
1250th term= 6 + (1249*2)= 2504
median= (2500 + 2504)/2 = 2502
do clarify thxs
My apologies, calculation error.
The total numbers should be 500 numbers indeed.
The previous method I have given was heavily flawed as I was being pestered by my students yesterday, and wasn't paying ample attention.
The correct way to find the median should be as followed:
For odd amount of numbers, you will have to divide it by 2, and then add 1/2 to it.
Eg. 151/2 = 75.5 , 75.5 + 0.5 = 76. Hence, median = 76th number.
For even amount of numbers, you will have to divide it by 2, find the next number in sequence, and get the average of these two.
Eg. 150/2 = 75, Median = ( 75th number + 76th number ) / 2
In this case, the total amount of numbers is 2498, which is an even amount.
2498/2 = 1249
The median will be ( 1249th number + 1250th number ) / 2
1249th number = 6 + ( 1248 X 2 ) = 2502
1250th number = 2504
Median = ( 2502 + 2504 ) / 2 = 2503
hi bro forbidden, i like to consult u
if a set of numbers (6,7,8....4999) and i get the median term as 2497.1(hypothetical answer)
so i should look at the term before 2497.1 and after 2497.1, so as to get the average of the 2 numbers to find the median
then i look at 2497th term and 2498th term, to c what number they correspond to.
my question is: if the median term is 2497.2, 2497.3, 2497.4, 2497.5, 2497.6, 2497.7, 2497.8 or 2497.9, do we still look at the 2497th term and 2498th term?
thxs
Originally posted by Divanhot:hi bro forbidden, i like to consult u
if a set of numbers (6,7,8....4999) and i get the median term as 2497.1(hypothetical answer)
so i should look at the term before 2497.1 and after 2497.1, so as to get the average of the 2 numbers to find the median
then i look at 2497th term and 2498th term, to c what number they correspond to.
my question is: if the median term is 2497.2, 2497.3, 2497.4, 2497.5, 2497.6, 2497.7, 2497.8 or 2497.9, do we still look at the 2497th term and 2498th term?
thxs
6, 7, 8 ,9 ,10.... 2497.1, 2497.2, 2497.3, 2497.4 .... 4999
That is an interesting pattern you have.
The 1st and foremost step is to find the total amount of numbers.
If there are 5555 numbers ( odd amount ) in all, the median term will be the ( (5555/2) + 0.5) term, which will be the 2778th term. Assuming that the 2778th number in the sequence is 2497.1, 2497.1 will be the median.
But if there are 5556 numbers ( even amount ) in all, the median term will be the average of the (5556/2) term and the term after it. In short, the median will be the average of the 2778th and the 2779th term. Assuming that the 2778th term is 2497.1, and the 2779th term is 2497.2, the median will be 2497.15.
Lets look at this sequence :
1,2,3,4,4.1,4.2,4.3,4.4,4.5,4.6,4.7,4.8,4.9,5.0,10,15,20,25,30,35,40,50,60,100,150,200.
If you calculate, there are 26 numbers in all.
The median will be the average of the 13th and the 14th term, regardless of how big the final number is, or how the pattern goes about.
In this case, the median will be ( 4.9 + 5.0 ) / 2, which is 4.95.
Compared to the last number in sequence, which is 200, 4.95 is quite a small number, but nevertheless, it is still the median.
hi bro, i think u misunderstand my question..
is it for all questions regarding median, after finding median position, we get the term before and after the median, in order to find the number corresponding to the term,
then we use the average of the 2 numbers to get the median.
but say if median now found is 2497.1( a fake number), and set of numbers from 6,7,8.... 4999. order is +1 number increasing.
do i look at the 2496th term and 2498th term?
if that is the case, if median term is one of the following:
2497.2 or 2497.3 or 2497.4 or 2497.5 or 2497.6 or 2497.7 or 2497.8 or 2497.9,
do we still use the 2496th term and 2497th term to find the median?
Originally posted by Divanhot:hi bro, i think u misunderstand my question..
is it for all questions regarding median, after finding median position, we get the term before and after the median, in order to find the number corresponding to the term,
then we use the average of the 2 numbers to get the median.
but say if median now found is 2497.1( a fake number), and set of numbers from 6,7,8.... 4999. order is +1 number increasing.
do i look at the 2496th term and 2498th term?
if that is the case, if median term is one of the following:
2497.2 or 2497.3 or 2497.4 or 2497.5 or 2497.6 or 2497.7 or 2497.8 or 2497.9,
do we still use the 2496th term and 2497th term to find the median?
Interesting question, but fortunately it will never happen.
If you divide a whole number by 2, there will only be 2 possible outcomes, either another whole number, or a number with a 0.5 decimal.
Hence, I cannot answer your question, as it is not possible for it to happen.
thxs bro for answering my queries.
attached is a snapshot of a cumulative frequency table.
http://img401.imageshack.us/i/plantsw.jpg/
for this case, if we apply median term= (64+1)/2= 32.5 term, which lies between 32th and 33th term,
so what is the 32th term and 33th term correspond to what height?
The question asks us to plot height(yaxis) against plants(xaxis)
my way of getting the median is to use 50%* 64=32 plants, then look at xaxis(height) to get answer
if use (n+1)/2, how to get median?
Originally posted by Divanhot:thxs bro for answering my queries.
attached is a snapshot of a cumulative frequency table.
http://img401.imageshack.us/i/plantsw.jpg/
for this case, if we apply median term= (64+1)/2= 32.5 term, which lies between 32th and 33th term,
so what is the 32th term and 33th term correspond to what height?
The question asks us to plot height(yaxis) against plants(xaxis)
my way of getting the median is to use 50%* 64=32 plants, then look at xaxis(height) to get answer
if use (n+1)/2, how to get median?
You mean the y-axis.
I will answer both of your questions together. After you realised the median is technically the 32.5th term, draw out the graph first. On the x-axis, find the point representing the 32.5th plant, then draw a straight line perpendicular to the x-axis up to the graph you have drawn. From the point which touches the graph, draw another straight line perpendicular to the y-axis towards the y-axis. The point which touches the y-axis will be your median height.
hi the plants are plotted on the y axis and the heights are plotted on the x axis.
attached is my working graph. i understand what you mean. look at the 32.5 term of plant on y axis and find the corresponding median height on the x axis
http://img196.imageshack.us/i/83016747.jpg/
but the answer i obtained is 51.5cm(but answer is wrong)
while if i use graph method: 50%* 64= 32 plants. median= 51cm, which is the correct answer.
i am confused as if use (n+1)/2 to find median, median=51.5cm
but if use graph method(which is n/2, 50th percentile), median= 51cm
Originally posted by Divanhot:hi the plants are plotted on the y axis and the heights are plotted on the x axis.
attached is my working graph. i understand what you mean. look at the 32.5 term of plant on y axis and find the corresponding median height on the x axis
http://img196.imageshack.us/i/83016747.jpg/
but the answer i obtained is 51.5cm(but answer is wrong)
while if i use graph method: 50%* 64= 32 plants. median= 51cm, which is the correct answer.
i am confused as if use (n+1)/2 to find median, median=51.5cm
but if use graph method(which is n/2, 50th percentile), median= 51cm
Generally speaking, since your scale is quite small, where 1 small box = 1cm, the margin for error should be +/- 1.0, and thus any answer from 50cm to 52cm should be acceptable.
But this is also dependent on how your teacher wish to mark your paper.
As for the median, the steps for finding it won't change just because we are drawing it on graph instead of calculating it out on paper.
For a total of 64 plants, the median will always be 32.5, as long as the amount of plants do not change.
