Why do we use n/2 to find the median of continuous data but (n+1)/2 for continuous?

I'm in Year 12, currently doing S1. The teacher has taught has that to find the median of a set of continuous or grouped discrete data, we use n/2 and to use (n+1)/2 when it is discrete.

However, I don't understand why. For example, say there's a set of data for hair length.

34 37 38 40

If we use n/2, surely the median would be 37? But that looks wrong?
But if you look at a cumulative frequency graph, the median is found at half of the total...

I don't understand why n/2 is right, please help :frown:

(edited 7 years ago)

Reply 1

the bear

20

i think it is to do with set sizes... if you have 600 pieces of data then n/2 is pretty similar to { n+1 }/2

Reply 2

TKLovesScience

OP

9

Original post by the bear

i think it is to do with set sizes... if you have 600 pieces of data then n/2 is pretty similar to { n+1 }/2

I don't see why it should mean that we should use 2 different ways to find the median though

Reply 3

HapaxOromenon3

3

Original post by TKLovesScience

I don't see why it should mean that we should use 2 different ways to find the median though

Actually the median is always defined as the (n+1)/2_th data point, so your teacher is wrong. See http://mathworld.wolfram.com/StatisticalMedian.html

Reply 4

TKLovesScience

OP

9

Original post by HapaxOromenon3

Actually the median is always defined as the (n+1)/2_th data point, so your teacher is wrong. See http://mathworld.wolfram.com/StatisticalMedian.html

This site says otherwise though... Most places I've looked say it depends on what type of data you're working with, but I don't know why

http://www.mrbartonmaths.com/resources/a%20level%20revision/S1.pdf

Reply 5

HapaxOromenon3

3

Original post by TKLovesScience

This site says otherwise though... Most places I've looked say it depends on what type of data you're working with, but I don't know why

http://www.mrbartonmaths.com/resources/a%20level%20revision/S1.pdf

As far as I know, it's always (n+1)/2. I can't speculate on why other sources have it incorrect...

Reply 6

username1162972

18

Original post by HapaxOromenon3

As far as I know, it's always (n+1)/2. I can't speculate on why other sources have it incorrect...

It is different convention iirc between exam boards or some **** like that.
Don't hold me accountable for that, this is back in my S1 days when I used the net to revise I figured this.

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Reply 7

T_T122

4

both n+1/2 and n/2 would be estimates for continuous data as no exact values so no notable difference

Why do we use n/2 to find the median of continuous data but (n+1)/2 for continuous?

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