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

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    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
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    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
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    (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
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    (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
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    (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/resourc...evision/S1.pdf
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    (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/resourc...evision/S1.pdf
    As far as I know, it's always (n+1)/2. I can't speculate on why other sources have it incorrect...
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    (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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