Why do we add 1 when working out median? Watch

foxstudy
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e.g. 80+1 /2
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Muttley79
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(Original post by foxstudy)
e.g. 80+1 /2
Do you mean when finding which value?

2, 3, 4, 6,7 The median is 4 the third value - (5 + 1)/2 = 3

7, 8, 10, 14, 15, 18 The median is 12, the average of the middle two - (6+ 1)/2 = 3.5 ie between the third and 4th.
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foxstudy
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(Original post by Muttley79)
Do you mean when finding which value?

2, 3, 4, 6,7 The median is 4 the third value - (5 + 1)/2 = 3

7, 8, 10, 14, 15, 18 The median is 12, the average of the middle two - (6+ 1)/2 = 3.5 ie between the third and 4th.
Yeah but if we had to find for example- the median using a histogram, in my book to find the median value, I first did total frequency +1 and /2 and then... but is that only with even numbers ? Like I don't understand.
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Muttley79
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(Original post by foxstudy)
Yeah but if we had to find for example- the median using a histogram, in my book to find the median value, I first did total frequency +1 and /2 and then... but is that only with even numbers ? Like I don't understand.
OK so for 99 values - the middle value is the 50th [(99 + 1)/2]. That's how I explain it - add 1 to the frequency then divide by 2 for all numbers odd and even.

To be honest many GCSE question seem to ignore this as on a CF curve the difference between 50th and 51st values is minimal.
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foxstudy
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(Original post by Muttley79)
OK so for 99 values - the middle value is the 50th [(99 + 1)/2]. That's how I explain it - add 1 to the frequency then divide by 2 for all numbers odd and even.

To be honest many GCSE question seem to ignore this as on a CF curve the difference between 50th and 51st values is minimal.
This is A level and they seem to have added 1 and then /2 with pretty much everything despite being odd or even. I don't really understand the point of this.
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Muttley79
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(Original post by foxstudy)
This is A level and they seem to have added 1 and then /2 with pretty much everything despite being odd or even. I don't really understand the point of this.
It's so you know which data value is in the 'middle' -

As I said for 99 values we want the 50th .... 49 values MEDIAN 49 values. If we just divide 99/2 we get 49.5 which is not the 'middle'

Just write a few lists of numbers and see why you always need to + 1 and divide by 2 to get which 'data' value is in the middle.

Even at A level the CF often is drawn without this sophistication.
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foxstudy
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(Original post by Muttley79)
It's so you know which data value is in the 'middle' -

As I said for 99 values we want the 50th .... 49 values MEDIAN 49 values. If we just divide 99/2 we get 49.5 which is not the 'middle'

Just write a few lists of numbers and see why you always need to + 1 and divide by 2 to get which 'data' value is in the middle.

Even at A level the CF often is drawn without this sophistication.
What about 50? ÷2 it gives us 25 but if you +1 we get a decimal??
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Muttley79
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(Original post by foxstudy)
What about 50? ÷2 it gives us 25 but if you +1 we get a decimal??
50 items of data - the median is (50 + 1)/2 = 25.5 ie the average of the 25th and 26th values - see my first post in this thread.
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foxstudy
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(Original post by Muttley79)
50 items of data - the median is (50 + 1)/2 = 25.5 ie the average of the 25th and 26th values - see my first post in this thread.
Oh my. I am so sorry for my stupidity. I just had a ping moment and all of this makes sense now! Btw I wasn't doing CF curves anyway but this all makes perfect sense now.
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Muttley79
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(Original post by foxstudy)
Oh my. I am so sorry for my stupidity. I just had a ping moment and all of this makes sense now! Btw I wasn't doing CF curves anyway but this all makes perfect sense now.
You aren't 'stupid' - many books (and teachers) just gloss over this ...
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