median & others

Divanhot SG

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

SBS 9613Z SG

firstly, what are the numbers in the set of numbers that you mentioned?

Divanhot SG

for square, are the diagonals equal in length and angle?

Mikethm SG

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

Mikethm SG

for square, are the diagonals equal in length and angle?

Yes.

Forbiddensinner SG

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

Divanhot SG

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

Divanhot SG

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?

Forbiddensinner SG

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.

Divanhot SG

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

Divanhot SG

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

dkcx SG

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

Mikethm SG

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.

Forbiddensinner SG

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

Divanhot SG

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

Forbiddensinner SG

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.

Divanhot SG

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?

Forbiddensinner SG

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.

Divanhot SG

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?

Forbiddensinner SG

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.