Median Formula Watch

personager
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I have come across two different median formulas:

1) (n+1)/2

2) n/2

and have been told to use the former when dealing with discrete data and the latter when dealing with continuous.

Therefore, would it be fair to say that when dealing with medians for frequency tables, stem and leaf diagrams, etc. it would be appropriate to use (n+1)/2 as those represent discrete data, where as when dealing with medians for grouped frequency tables, cumulative frequency graphs, histograms, etc. it would be appropriate to use n/2 as they represent continuous data.

I ask this because I came across an example in the Edexcel book where the formula n/2 has been used to find the median for a stem and leaf diagram and now I'm unsure whether what I have been told is correct or not.

Any help will be greatly appreciated.
Thanks
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Mr M
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It is about the size of the data set. With a large data set n/2 is a sufficiently good approximation for (n+1)/2 for it to make negligible difference to the answer.
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ExWunderkind
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(Original post by personager)
I have come across two different median formulas:

1) (n+1)/2

2) n/2

and have been told to use the former when dealing with discrete data and the latter when dealing with continuous.

Therefore, would it be fair to say that when dealing with medians for frequency tables, stem and leaf diagrams, etc. it would be appropriate to use (n+1)/2 as those represent discrete data, where as when dealing with medians for grouped frequency tables, cumulative frequency graphs, histograms, etc. it would be appropriate to use n/2 as they represent continuous data.

I ask this because I came across an example in the Edexcel book where the formula n/2 has been used to find the median for a stem and leaf diagram and now I'm unsure whether what I have been told is correct or not.

Any help will be greatly appreciated.
Thanks
Mr M has the ken.

If you think about the +1, you realise that in datasets of 000s it would be negligible difference. If it's just 10, it makes a lot of difference.
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personager
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(Original post by Mr M)
It is about the size of the data set. With a large data set n/2 is a sufficiently good approximation for (n+1)/2 for it to make negligible difference to the answer.
(Original post by ExWunderkind)
Mr M has the ken.

If you think about the +1, you realise that in datasets of 000s it would be negligible difference. If it's just 10, it makes a lot of difference.
I see. But when I use n/2 in small data sets, I get a significantly different answer as compared to the answer I get when using (n+1)/2. Which one should I use?
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Mr M
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(Original post by personager)
I see. But when I use n/2 in small data sets, I get a significantly different answer as compared to the answer I get when using (n+1)/2. Which one should I use?
(n+1)/2 as I previously explained.
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ExWunderkind
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(Original post by personager)
I see. But when I use n/2 in small data sets, I get a significantly different answer as compared to the answer I get when using (n+1)/2. Which one should I use?
Exactly that's the point we're making, you will get a big difference with small data sets. Thus, when the data set is small use (n+1)/2.
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Robbie242
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(Original post by Mr M)
(n+1)/2 as I previously explained.
Also I apoligise if you've confirmed this before but for the upper quartile is it \frac{3(n+1)}{4} or \frac{3n+1}{4}
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Sammy-Boy-206
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(Original post by Robbie242)
Also I apoligise if you've confirmed this before but for the upper quartile is it \frac{3(n+1)}{4} or \frac{3n+1}{4}
First for small data sets, second for large
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ExWunderkind
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(Original post by Robbie242)
Also I apoligise if you've confirmed this before but for the upper quartile is it \frac{3(n+1)}{4} or \frac{3n+1}{4}
I always say 3/4(n+1) so there's no confusion.
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Robbie242
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(Original post by Sammy-Boy-206)
First for small data sets, second for large
Sorry if this is a dumb question (and I full well know that it is) What is the difference between a small data set and a large data set? Thanks, also would it be Q_1=\frac{n+1}{4} for small data sets and Q_1=\frac{n}{4} for large data sets
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Sammy-Boy-206
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(Original post by Robbie242)
Sorry if this is a dumb question (and I full well know that it is) What is the difference between a small data set and a large data set? Thanks, also would it be Q_1=\frac{n+1}{4} for small data sets and Q_1=\frac{n}{4} for large data sets
Answer to first question is that I honestly would not know. The difference in using the two formulas will become smaller and smaller as the data set increases in size. I'm an engineer not a statistician so can't be any more help than that And to answer your second question, yeah that's correct.
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personager
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(Original post by ExWunderkind)
Exactly that's the point we're making, you will get a big difference with small data sets. Thus, when the data set is small use (n+1)/2.
(Original post by Mr M)
(n+1)/2 as I previously explained.
I thought so, however when doing questions from the text book, one of which asks me to find the median of 21 sets of data, the answer stated at the back of the book is one that I get one by using n/2 rather than (n+1)/2.
Similarly, the same question then goes on to ask the upper quartile and using the formula 3(n+1)/4 gives the wrong answer as the answer stated in the book is the answer I would get by using 3n/4
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Robbie242
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(Original post by Sammy-Boy-206)
Answer to first question is that I honestly would not know. The difference in using the two formulas will become smaller and smaller as the data set increases in size. I'm an engineer not a statistician so can't be any more help than that And to answer your second question, yeah that's correct.
Alright thanks, would you know what form such data sets come in, so I can easily recognise them, e.g. cumlulative tables, an array of numbers, frequency tables, discrete tables, class boundary tables etc.
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Sammy-Boy-206
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(Original post by Robbie242)
Alright thanks, would you know what form such data sets come in, so I can easily recognise them, e.g. cumlulative tables, an array of numbers, frequency tables, discrete tables, class boundary tables etc.
Any I would of thought
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Robbie242
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(Original post by Sammy-Boy-206)
Any I would of thought
Ok now I'm confused, so I can use either formula and get the marks?
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personager
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When asked to find the median of a small set of discrete data (say 20 pieces of data represented on a stem and leaf diagram), I use the (n+1)/2 formula and get the 18.75th term as the answer. Would I round it down to 18.5 and therefore find the mean of the 18th and 19th terms to obtain the answer? Or is this incorrect and should I go about it some other way?
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Robbie242
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(Original post by personager)
When asked to find the median of a small set of discrete data (say 20 pieces of data represented on a stem and leaf diagram), I use the (n+1)/2 formula and get the 18.75th term as the answer. Would I round it down to 18.5 and therefore find the mean of the 18th and 19th terms to obtain the answer? Or is this incorrect and should I go about it some other way?
I've generally done it this way and its seen to be correct, with quartile parts e.g. 18.75, you round up to 19

but if its halfway between two terms 18.5 lets say, you add both terms on each side up and divide by two and round if necessary
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Mr M
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(Original post by Robbie242)
Sorry if this is a dumb question (and I full well know that it is) What is the difference between a small data set and a large data set? Thanks, also would it be Q_1=\frac{n+1}{4} for small data sets and Q_1=\frac{n}{4} for large data sets
How long is a piece of string?

And yes.
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Mr M
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(Original post by personager)
I thought so, however when doing questions from the text book, one of which asks me to find the median of 21 sets of data, the answer stated at the back of the book is one that I get one by using n/2 rather than (n+1)/2.
Similarly, the same question then goes on to ask the upper quartile and using the formula 3(n+1)/4 gives the wrong answer as the answer stated in the book is the answer I would get by using 3n/4
Perhaps they don't care what you put as your answer? You don't seem to have discovered yet that much of statistics is mathematical woo-woo.

15 different ways to calculate quartiles:

http://www.amstat.org/publications/j.../langford.html
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